Answer:
[tex]y=-11x-16[/tex]
Step-by-step explanation:
We want to find the equation of the tangent line to the function:
[tex]f(x)=4x^2+5x[/tex]
At the point (-2, 6).
First, we will need the slope of the tangent line. So, differentiate* the function:
[tex]f'(x)=8x+5[/tex]
Find the slope when x = -2:
[tex]f'(-2)=8(-2)+5=-11[/tex]
Now, we can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Our point is (-2, 6) and our slope is -11. Substitute:
[tex]y-(6)=-11(x-(-2))[/tex]
Simplify:
[tex]y-6=-11(x+2)[/tex]
Distribute:
[tex]y-6=-11x-22[/tex]
And add six to both sides. Therefore, our equation is:
[tex]y=-11x-16[/tex]
If you have not yet learned differentiation, here's the method using the difference quotient! The difference quotient is given by:
[tex]\displaystyle f'(x)=\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}[/tex]
Here, x = -2. Substitute:
[tex]\displaystyle f'(-2)=\lim_{h\to 0}\frac{f(-2+h)-f(-2)}{h}[/tex]
Substitute (we are given the point (-2, 6). So, f(-2) = 6).
[tex]\displaystyle f'(-2)=\lim_{h\to 0}\frac{(4(-2+h)^2+5(-2+h))-(6)}{h}[/tex]
Expand and simplify:
[tex]\displaystyle f'(-2)=\lim_{h\to 0}\frac{(4(4-4h+h^2)+(-10+5h))-(6)}{h}[/tex]
Distribute:
[tex]\displaystyle f'(-2)=\lim_{h\to 0}\frac{16-16h+4h^2-10+5h-6}{h}[/tex]
Simplify:
[tex]\displaystyle f'(-2)=\lim_{h\to 0}\frac{4h^2-11h}{h}[/tex]
Evaluate the limit (using direct substitution):
[tex]\displaystyle f'(-2) = \lim_{h\to 0}4h-11=4(0)-11=-11[/tex]
At 9:30 am, Hudson and Colin leave on a bicycle trip. Their average speed is 20 km/ h. At 11:30 am, Danielle leaves from the same place and starts driving after them in her car. Her average speed is 60 km/ h. Create a system to determine how long will it take Danielle to catch up with Hudson and Colin?
Answer:
Step-by-step explanation:
11:30-9:30=2
so Danielle starts 2 hrs late.
let Danielle catches them after x hrs.
x×60=(x+2)×20
divide by 20
3x=x+2
3x-x=2
2x=2
x=1
so Danielle takes 1 hour to catches them.
Rewrite in simplest rational exponent form √x • 4√x
Answer:
4x
Step-by-step explanation:
[tex]\sqrt{x} \cdot \sqrt{x} = \sqrt{x^2} = x^{ 2 \times \frac{1}{2}} = x[/tex]
[tex]given :\\\\ \sqrt{x} \cdot 4\sqrt{x} = 4 \cdot\sqrt{x} \sqrt{x} = 4 \sqrt{x^2} = 4x[/tex]
find the equation of a line that passes through (3 1) and ia parallel to y=1-2x leave your answer in the form of y=mx+c
Answer:
y = -2x+7
Step-by-step explanation:
Parallel lines have the same slope
y = 1-2x has a slope of -2
So the new line has a slope of -2
We have a slope of -2 and a point of (3,1)
y = mx+c
1 = -2(3)+c
1 = -6+c
Add 6 to each side
1+6 =c
7 =c
y = -2x+7
make x the subject of the formula
y=a√x
Answer:
y=a√x
y/a=a√x/a a will cancel out on the right side of the equation
therefore, √x=y/a
x=√y/x
What is the slope of a line that is perpendicular to the line y =1/2x+5?
-2
-1/2
1/2
2
Answer:
[tex] - 2[/tex]
Step-by-step explanation:
Hope it is helpful...
17.
Write the equation in standard form. Then factor the left side of the equation.
2x2 + 7x = 15
A. (2x – 5)(x + 3) = 0
B. (2x + 3)(x + 5) = 0
C. (2x – 3)(x + 5) = 0
D. (2x + 5)(x – 3) = 0
Answer:
C. (2x – 3)(x + 5) = 0
Step-by-step explanation:
The equation in standard form should be 2x^2 + 7x - 15 = 0
Factored the expression is (2x - 3)(x + 5).
In order to find the factored portion, you must look for factors of the front number (2) to use in the front of the parenthesis and factors of the last number (-15) to go in the end.
When we use the ones that we have above, it distributes to the overall end result.
(2x - 3)(x + 5)
2x^2 - 3x + 10x - 15
2x^2 + 7x - 15
what is the solution to the equation 1/4 x + 2 -5/8 x - 5? i
Answer:
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Answer both for brainly pro
Find the surface area of the figure using its net
how long will they take to make 504 muffins if they will be using 4 ovens?
Answer:
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Q. The ratio 12:27 simplified to the form 1:n is *
a-1:2.25
b-1: 0.4
Answer:
1:2.25
12/12 = 1
27/12 = 2.25
Hope this helps!
En la inaguracion de unos juegos olimpicos, los 38 representantes de una nacion quieren desfilar formando columnas de 6¿es posible?¿de que modo podria desfilar formando columnas iguales?
Answer:
a) No
b) Sí
Step-by-step explanation:
a) En la inauguración de unos Juegos Olímpicos, los 38 representantes de una nación quieren desfilar en columnas de 6, ¿es posible?
Esto se calcula como
38 representantes / 6 columnas
= 6 2/6 = 6 1/3 columnas
No, no es posible, tendríamos 7 columnas con 6 columnas con representantes iguales de 6 y la séptima columna tendría solo 2 representantes allí
b) ¿Cómo podrían desfilar en columnas iguales?
Sí pueden
Esto se calcula como 38 representantes ÷ 2
= 19 columnas
Podemos tener 19 columnas con 2 representantes cada una
The perimeter of a rectangle is 80x. The base is 7 times the height. In terms of x, what are the dimensions of the rectangle?
a.
h = 10x, b = 10x
c.
h = 3x, b = 5x
b.
h = 5x, b = 35x
d.
h = 5x, b = 25x
B E
400
(51)
А
C D
3t
Find the measure of ZF if mZD=88º.
A. 8°
B. 40°
C. 52°
D. 90°
the answer is c because you have to take the zf an time it by the zd
Answer:
C
Step-by-step explanation:
for the top of the triangle it has to be 40 and angle d has been declared as 88
so it is 40+88 = 128 now 180 -128 = 52 so the answer is C
land value is increased by 12 % in each year in 2016 , the value is $60000.
i )what us the land value after 4 years
ii) Calculate the increase of the land value during these 4 years.
Answer:
I=use PTR/100
ii =p+i
Step-by-step explanation:
hope you like it
Lexon is standing 7.05 meters away from the statue off the Merlin mp at Merlin park Singapore the height of her eyes from her feet is 1.55 meters given that the angle of elevation of the top of the statue from her eyes is 42ﾟ find the height of the statue
Answer:
7.9m
Step-by-step explanation:
We solve using the Trigonometric function of Tangent
tan θ = Opposite/Adjacent
Opposite = x
Adjacent = 7.05m
We solve for x
tan 42 = x /7.05m
Cross Multiply
tan 42 × 7.05 = x
x = 6.3478485123m
Approximately = 6.35m
Height of the statue = x + 1.55
Hence, = 6.35m + 1.55m
= 7.9m
The height of the statue = 7.9 meters
SOMEONE PLEASE HELP ME I DONT KNOW HOW TO DO THIS TYPE OF PROBLEM
Answer:
Step-by-step explanation:
Because angles SQR and RQT are central angles, they are congruent to the arcs they intercept. This means that arc SR = 101 and arc RT = 118, making the whole major arc SRT = 219. That means that the minor arc, ST is 360 - 219 which is 141. We are looking in particular for the measure of angle SRT. It just so happens that angle SRT is an inscribed angle, so by definition it is one-half the measure of the arc it intercepts. It intercepts arc ST which we found measures 141, so angle SRT is 141/2 = 70.5
Given m||n, find the value of x.
(7x-4)
(3x+28)º
Answer:
8
Step-by-step explanation:
7 x 8 = 56 56 - 4 = 52.
3 x 8 = 24 24 + 28 = 52
A North American river otter wants to cross the North Saskatchewan river. It can swim at a speed of 2.75 m/s. In that location, the distance directly across the river is 45.0 m and the current velocity is 2.5 m/s.
a) How much time does the otter take to get to the other side, if it points directly across the river?
Answer:
time=16.3 sec
Step-by-step explanation:
let time taken be x
speed=distance/time taken
2.75=45/x
2.75x=45
x=45/2.75
x=16.36
x=16.3 seconds
The time taken is 16.3 seconds.
What is speed?Speed = Distance/Time
This informs us how slowly or quickly an object moves. It defines the distance traveled divided by the time brought to cover the distance. Speed stands directly proportional to distance and inversely proportional to Time.
Let x be the time taken
speed = distance/time taken
2.75 = 45/x
2.75x = 45
x = 45/2.75
x = 16.36
x = 16.3 seconds
Therefore, the time taken is 16.3 seconds.
To learn more about speed
https://brainly.com/question/21904438
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Please help I’ll give brainliest
Answer:
B. $180
Step-by-step explanation:
3/2 × $120 = $180
______
Help me find the answer for this Acellus question! Find CD.
Answer:
DE = AE - AD
=> DE = 18.5 - 15.5 = 3
CD = CE - DE = 8 - 3 = 5
Help this is confusing
If the circumference of a circle is 10π inches, what is the area, in square inches, of the circle?
Answer:
25π square inches or 78.5 sq in
Step-by-step explanation:
circumference = π x diameter
thus
10 π inches= π x d
d = 10 inches
area of circle = π x d x d / 4
= π x 10 x 10 x 4
= 25π sq in
= 78.5 sq in
HELP WILL GIVE BRAINLIEST SHOW WORK LOOK AT IMAGE
Answer:
Step-by-step explanation:
which statement would be true if you evaluate the expression 15x(465x4)
a. the solution is 5 times as small as 3x(465x4)
b. the solution is 3 times as small as 3x(465x4)
c. the solution is 3 times as large as 5x(465x4)
d. the solution is 3 times as large as 5x(465+4)
Answer:
c. the solution is 3 times as large as 5x(465x4)
Step-by-step explanation:
I assume you are using the letter x as the multiplication sign.
Start with:
15 x (465 x 4)
We know that 15 = 3 x 5
Now we replace 15 with 3 x 5 in the original expression.
15 x (465 x 4) = 3 x 5 x (465 x 4)
Answer: c. the solution is 3 times as large as 5x(465x4)
[tex]-2\sqrt{50x^5} +5\sqrt{18x^5}[/tex]
Answer:
234.98
Step-by-step explanation:
in class notes
which equation has x=4 as the solution
Which graph represents the solution set of the inequality x + 2 greater-than-or-equal-to 6 A number line goes from negative 9 to positive 9. A solid circle appears on positive 3. The number line is shaded from positive 3 through negative 9. A number line goes from negative 9 to positive 9. An open circle appears at positive 3. The number line is shaded from positive 3 through positive 9. A number line goes from negative 9 to positive 9. A closed circle appears at positive 4. The number line is shaded from positive 4 through positive 9. A number line goes from negative 9 to positive 9. An open circle appears at positive 4. The number line is shaded from positive 4 through negative 9.
Colin and Dan win some money and share it in the ratio 4:5. Colin gets £52. How much did they win in total?
Answer:
$65
Step-by-step explanation:
Collin gets 4x dollars which equals 52, so 4x = 52
Dan gets 5x dollars which equals y (the answer). solve for x = 13. 5 • 13 = 65.
what is the possibility of a two sided coin flipped and lands on tails?
Answer:
Step-by-step explanation:
it has a 50/50 chance if it lands on tailes it is 50/50
