Answers
Answer:
gradient = 9
Step-by-step explanation:
The gradient of the tangent at x = a is the derivative [tex]\frac{dy}{dx}[/tex]
Differentiate using the power rule on each term
[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] and [tex]\frac{d}{dx}[/tex] ( constant ) = 0
y = 2x² + 5x - 3
[tex]\frac{dy}{dx}[/tex] = 2.2[tex]x^{2-1}[/tex] + 5[tex]x^{1-1}[/tex] - 0
= 4x + 5
[tex]\frac{dy}{dx}[/tex] ( x = 1 ) = 4(1) + 5 = 4 + 5 = 9 ← gradient of tangent
Related Questions
Write the equation of a line parallel to the line y = 2x that passes through 0,4
Answers
Note: this answer assumes that the question accepts the equation to be written in slope-intercept form.
Answer:
y = 2x + 4
Step-by-step explanation:
To write an equation of a line knowing a slope and a y-intercept, you can use slope-intercept form, or y = mx+ b.
1) Lines that are parallel to each other have the same slope. The answer needs to be parallel to the line y = 2x, so whatever the slope of that equation is must be the slope of the answer, too.
y is isolated in y = 2x, meaning it is in slope-intercept form, or y = mx +b form. The m in y = mx + b represents the slope of the line. In the equation y = 2x, the 2 is in the place of that m - meaning that 2 is the slope of that line, and therefore the slope of the answer, too.
2) The question also says that (0,4) is a point the line must pass through as well. However, notice that the x-value of the point is 0, meaning it is positioned on the y-intercept. Therefore, (0,4) must be the y-intercept of the equation.
3) To write a linear equation with y = mx + b form, you need to replace the m and the b for real values. The slope is 2, and m represents the slope - so write 2 in place of the m. The b represents the y-value of the y-intercept point - knowing that point is (0,4), write 4 in place of the b. Therefore, the answer would be y = 2x + 4 (assuming the question can be written in slope-intercept form).
a dolphin swam 12 miles in 4 hours. what was its average speed in miles per hour (mph) ?
Answer choices : A. 2 mph
B . 4 mph
C. 3 mph
D. 7 mph
PLEASE HELLPPP :(
Answers
An elevator is on the 15th floor. it goes down eight floors. What floor is the elevator on now?
Answers
Answer:
7
Step-by-step explanation:
15 - 8 = 7
She said I drove her away with my emotions
Answers
Select all the equations that have x=4 as the solution *
A 42 = 38 + x
B x + 15 = 19
C 18 = x - 2
D 32 = 36 - x
E 52 - x = 46
Answers
Answer:
A B D
Step-by-step explanation:
A 38+4=42
B 4+15=19
C 18= 20-2
D 32= 36-4
E 52-6=46
A gardener wants to build a rectangular fence for his prize winning roses. The length of the fence should be at least 6 feet and the distance around it should be no more than 18 feet. What are the possible dimensions?
Answers
Answer:
Dimension = 6 feet × 3 feet
Step-by-step explanation:
From the question given above, the following data were obtained:
Length (L) = 6 feet
Distance around the fence (Perimeter) = 18 feet
Dimension of the fence =?
Next, we shall determine the breadth of the rectangular fence. This can be obtained as follow:
Length (L) = 6 feet
Perimeter (P) = 18 feet
Breadth (B) =?
Perimeter of rectangle is given by:
P = 2(L + B)
18 = 2 (6 + B)
Clear the bracket
18 = 12 + 2B
Collect like terms
18 – 12 = 2B
6 = 2B
Divide both side by 2
B = 6/2
B = 3
Thus, the breadth of the rectangular fence is 3 feet
Dimension of the rectangular fence is given by:
Dimension = length × Breadth
Length (L) = 6 feet
Breadth (B) = 3 feet
Dimension = 6 feet × 3 feet
Which of the following rational functions is graphed below?
Answers
Answer: Choice C [tex]f(x) = \frac{1}{x(x+4)}[/tex]
========================================================
Explanation:
The vertical asymptotes are the red dashed lines. They are x = -4 and x = 0. Think of them as electric fences that the graph cannot touch or cross. The curve can only get closer and closer.
The vertical asymptote is due to a division by zero error.
When x = 0, the denominator x(x+4) turns into 0 since
x(x+4) = 0(0+4) = 0*4 = 0
Similarly, when x = -4, the denominator is also zero
x(x+4) = -4(-4+4) = -4*0 = 0
So if x = -4 or x = 0, then we have a division by zero error and that's what produces the vertical asymptotes at those locations shown on the graph.
This is why the answer is choice C. [tex]f(x) = \frac{1}{x(x+4)}[/tex]
Maria and her friends ordered a pizza that cost $14.70. She paid $2.94 for her part. What percent of the total bill did she pay?
Answers
Answer:
14.70-2.94 = 11.76
11.76/14.70 = 0.8
0.8 X 100 = 80
100 - 80 = 20%
Factor the quadratic expression completely.
2x2 + 7x + 3
Answers
Answer:
(2x+1)(x+3)
Step-by-step explanation:
just remember to put a ^ when you do this 2x2 put it like this 2x^2
an you welcome and plz give me brainiest
Find the vault of each variable
Answers
Explanation:
Since it’s a 45-45-90 degree triangle
The two lengths are equivalent to each other and the hypotenuse is equal to the length multiply by sqrt(2).
Thus x = 13 and y = 13sqrt(2)
Which of the following is equal to the product of 32 and 1/4 ?
Answers
Hey there!
The answer to your question is 8
In math, the "product of" represents multiplication, so we multiply the 2 numbers.
32 x 1/4 = 8
Hope this helps! Good luck, and have a great day!
A = Pert
A small forest has 30 rabbits and grows continuously
at a rate of 60%. How many rabbits do you expect to
see in this forest after 5 years? Round your answer to
the nearest whole rabbit.
PLZZZZZZZZ HELP ASAP ND THANK YOU
Answers
========================================================
Work Shown:
P = 30 = initial populatione = 2.71828 = a constant (similar to pi = 3.14)r = 0.60 = growth rate in decimal formt = 5 = number of yearsApplying those values gets us the following
A = P*e^(r*t)
A = 30*2.71828^(0.60*5)
A = 602.56489
A = 603
After five years, there are approximately 603 rabbits in that forest.
The figure shows a truss used in the construction of a building. The measure of ∠1 is 39°. Find the measure of ∠2.
Answers
Answer:
39
Step-by-step explanation:
Since the first measure is 39 that means the second is 39 because its the same.
I need help with geometry
Answers
Answer:
ASA congruency and corresponding sides of congruent triangles are congruent
Step-by-step explanation:
The radius of the circle on a basketball court is 6 feet. What are the approximate
circumference and area of the circle?
Circumference: 37.7 feet
Area: 113.0 square feet
Circumference: 18.8 feet
Area: 37.7 square feet
Circumference: 18.8 feet
Area: 113.0 square feet
Circumference: 12.0 feet
Area: 18.8 square feet
Answers
Answer:
C= 37.69ft
A= 113.09ft
Step-by-step explanation:
Circumference=
=37.69
Area=
Area = pi * 6 ^2
Area =113.09
The graph shows the distance Julie walks over time. Does she walk at a constant or variable
speed? How fast
is Julie walking?
a. variable speed; 8 mi/h
b. constant speed; 2 mi/h
c. constant speed; 4 mi/h
d. constant speed; 8 mi/h
Answers
PLEASE HELP! YOU WILL GET 10 BRAINLIST!! PLEASE SHOW ALL OF YOUR WORK/HOW YOU GOT THE ANSWER
-2(y+4)-2y >8
Answers
Answer:
-2(y+4)-2y >8
-2y-8-2y>8
-4y-8>8
-4y<8+8
When you move a number on the other side it changes the side then > will become <
-4y<16
-4y/-4<16/-4
y<-4
9/4 divided by 3/8 what the answer?
Answers
Answer:
6
Step-by-step explanation:
A rectangular picture frame has side lengths of 12 in by 9.5 in what is the length of the diagonal of the picture
Answers
Answer:
Length of diagonal of picture = 15.30 inches
Step-by-step explanation:
Given that:
Side lengths of picture frame = 12 inches by 9.5 inches
As the picture is rectangular, the diagonal will form hypotenuse of right angled triangle.
Using Pythagorean theorem;
a²+b²=c²
Putting the values in the theorem
[tex](12)^2 + (9.5)^2 = c^2 \\144+90.25=c^2\\c^2 = 234.25[/tex]
Taking square root on both sides
[tex]\sqrt{c^2}=\sqrt{234.25}\\c=15.30[/tex]
Hence,
Length of diagonal of picture = 15.30 inches
PLS HELP ILL GIVE BRAINLIEST PLS PLS PLS EXPLAIN UR ANSWER
Answers
Answer:
the answer is C
Step-by-step explanation:
i Dont know the step by step explanation because im not smart
but the answer is C
There are 4 cups in a row from left to right. The green cup is somewhere between the yellow and blue cups. The red cup is somewhere left of the yellow cup. Based on that information, how many different arrangements of these cups could there be?
Answers
Answer:
Le answer tis 4 UwU
Step-by-step explanation: G'day mate!
P.S- Brainlest plzz??
Answer:
5
Step-by-step explanation:
e
Can someone help me with these answers please
Answers
Answer:
7. 7x
8. -2v+19
9. 8p-26
10. 14y-5
11. 7m-13
12. -8k+25
13. -3w-13
14. -9c+27
15. m+4n
16.-7s
17. 6x-13y-24
18. 6h-16b
19. -9p+9q+12
20. 2k/5+ 31/4
Step-by-step explanation:
a candy shop contains a total of 300 items there are 125 chocolates 97 cookies and T number of truffles write an equation that represents the situation
Answers
Given:
A candy shop contains a total of 300 items.
There are 125 chocolates 97 cookies and T number of truffles.
To find:
The equation for the given situation.
Solution:
We have,
Number of chocolates = 125
Number of cookies = 97
Number of truffles = T
Total items = [tex]125+97+T[/tex]
A candy shop contains a total of 300 items. So,
[tex]125+97+T=300[/tex]
Therefore, the required equation for the given situation is [tex]125+97+T=300[/tex].
Alex started reading her book for 2 hours and 35 minutes one day and finished by reading 1 hour 52 minutes the next day. how long did it take her to read the entire book?
Answers
Answer:
4hour and 27 minute to finsh the entire book
Step-by-step explanation:
Carrie is making a temporary ramp from the ground to the top of his patio so that he can roll a cart up to it to move furniture in. The surface of the patio is 3‘9“ above the ground and Gary wants the ramp to have a slope of no more than 0.375. What is the shortest horizontal distance he can have from the base of the patio to the base of the ramp
Answers
9514 1404 393
Answer:
10 ft
Step-by-step explanation:
The slope is rise/run. Using Gary's numbers, we have ...
m = rise/run
0.375 ≥ (3.75 ft)/run
run ≥ (3.75 ft)/0.375
run ≥ 10 ft
The shortest horizontal distance to the base of the ramp is 10 feet.
Can someone pleasee help or explain to me how u do this? I don’t really Understand ?
Answers
- meaning your line goes through quad 1 and quad 3
The rule for a reflection in the line y = x is :
( x, y ) —> ( y, x )
which in your case is:
( 4, 2 ) —> ( 2, 4 )
So the answer is (2,4)
express the ratio in its simplest form 12cm to the 2nd power :3m to the 2nd power
Answers
Answer:
16:1
plz brainliestt
Step-by-step explanation:
144 : 9
Answer:
16:1
Step-by-step explanation:
The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2,200 people enter the fair and $5,050 is collected. How many children and how many adults attended?
Answers
Given :
The admission fee at a small fair is $1.50 for children and $4.00 for adults.
On a certain day, 2,200 people enter the fair and $5,050 is collected.
To Find :
How many children and how many adults attended.
Solution :
Let, number of children and adults attended are c and a.
So, c + a = 2200 ....1)
Now, fair collected is given by :
1.5c + 4a = 5050 ....2)
Putting value of a from equation 1) to 2), we get :
1.5c + 4( 2200 - c ) = 5050
1.5c - 4c = 5050 - 8800
2.5c = 3750
c = 1500
a = 2200 - 1500
a = 700
Therefore, 1500 children and 700 adults attended the fair.
20 points
A large amount of peanuts was divided equally into 6 small bags. The total number of peanuts, p, was 342. Which
statements can be used to write an expression and then find the number of peanuts that ended up in each bag?
Check all that apply.
The operation is division.
The operation is multiplication.
The variable is the number of bags.
342 divided by 6 equals 57.
Write the division expression as a fraction,
To evaluate, substitute 342 for the variable.
Each bag will have 57 peanuts.
The constant is 342.
Answers
Answer:
I think the answer is A, D, E, F, and G.
Tell me if i'm right or wrong please.
Answer:
adefg
Step-by-step explanation:
What do these stand for
Answers
Answer:
Time and seconds
Step-by-step explanation:
I know its time and seconds because I go to school
Answer:
v(m/s) means velocity in meters per second and t(s) means time in seconds