Answer:
y = 1.
Step-by-step explanation:
f(x) = x^2 + 1
We know that:
[tex]f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]
replacing the function, we get:
[tex]f'(x) = \lim_{h \to 0} \frac{(x + h)^2 + 1 - (x^2 + 1)}{h} \\ = \lim_{h \to 0} \frac{(x + h)^2 - x^2}{h} \\\\ = \lim_{h \to 0} \frac{x^2 + 2xh + h^2 - x^2}{h} \\\[/tex]
Now we can simplify this to:
[tex]= lim_{h \to 0} \frac{ 2xh + h^2 }{h}[/tex]
and solving the quotient, we get:
[tex]= lim_{h \to 0} 2x + h = 2x + 0 = 2x[/tex]
then f'(x) = 2*x
And we want the equation for the tangent line at (0, 1)
The slope of that line will be:
f'(0) = 2*0 = 0
So this is a horizontal line, of the type y = a
And we know that this line must pass through the point (0, 1)
so we must have y = 1.
Then the equation of the tangent line to f(x) at the point (0, 1) is:
y = 1.
g At noon, ship A is 10 nautical miles due west of ship B. Ship A is sailing west at 17 knots and ship B is sailing north at 25 knots. How fast (in knots) is the distance between the ships changing at 4 PM
Answer:
[tex]\triangle d=47.69 Knots[/tex]
Step-by-step explanation:
Distance of Ship A from B [tex]d_1=10 West[/tex]
Speed of Ship A [tex]V_a=17 knots West[/tex]
Speed of Ship A [tex]V_b=25 knots North[/tex]
Generally the equation for Rate of distance change is mathematically given by
[tex]\triangle d=\frac{1}{2\sqrt{(17t+10)^2+(25t)^2}}*\triangle t[17t+10^2+25t^2][/tex]
[tex]\triangle d=\frac{578+340+1250}{2\sqrt{(17t+10)^2+(25t)^2}}[/tex]
Therefore with
t=>4PM
We substitute
[tex]\triangle d=\frac{882(4)+420+648(4)}{2\sqrt(21(4)+10^2)+(18(4))^2}[/tex]
[tex]\triangle d=47.69 Knots[/tex]
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!!
Answer:
pulling a king out of a deck of cards
Step-by-step explanation:
A compound event is more than one thing happening
The only item listed that has only one thing happening is pulling a king out of a deck of cards, so that is the only one that is not a compound event
Which expression results in the smallest difference?
A.12.5 - 3.1
B.12.5 -0.31
C.12.5 -0.031
D.12.5 -0.0031
Answer:
i pretty sure it is A
Step-by-step explanation:
Pls help
Escape Question 2
Answer:
unlock code is 11
A= 27
B=16
C=1
(11)^1 = 11
Step-by-step explanation:
It costs a total of R138.90 to purchase 10 loaves of bread and 12 litres of cooidrinks in a store. If the store raises the price of bread by 20% and the price of cooldrinks by 10%, the total price of these items becomes R159.54. Find the original price of three loaves of bread and two litres of cooldrinks.
9514 1404 393
Answer:
R32.15
Step-by-step explanation:
Let x and y represent the original price of a loaf of bread and a liter of drink, respectively. The two relations given by the problem statement are ...
10x +12y = 138.90
10(1.2x) +12(1.1y) = 159.54
Multiplying the first equation by 1.2 and subtracting the second gives ...
1.2(10x +12y) -(10(1.2x) +12(1.1y)) = 1.2(138.90) -(159.54)
1.2y = 7.14 . . . . collect terms
y = 5.95 . . . . . divide by 1.2
The value of x can be found from the first equation.
10x + 12(5.95) = 138.90
10x = 67.50 . . . . . . . . . . . subtract 71.40
x = 6.75 . . . . divide by 10
Then the value of 3x+2y is ...
3(6.75) +2(5.95) = 32.15
The original price of 3 loaves and 2 liters is R31.15.
How is the product of a complex number and a real number represented on the coordinate plane?
A. When 2+3i is multiplied by 3, the result is 6+9i. Graphically, this shows that the product is a scalar of the complex number.
B. When 2+3i is multiplied by 3, the result is 6+9i. Graphically, this shows that the product is a countercockwise rotation of 90 degrees of the complex number.
C. When 2+3i is multiplied by 3, the result is 6+9i. Graphically, this shows that the product is a clockwise rotation of 90 degrees of the complex number.
D. When 2+3i is multiplied by 3, the result is 6+9i. Graphically, this shows the product is a counterclockwise rotation of 90 degrees and a scalar of the complex number.
Please help I don't know which one.
Answer:
A
Step-by-step explanation: When you multiply a coordinate in the complex plane it doesn't just magically rotate. It works the exact same way a normal coordinate would. Therefore, the answer is A
When 2 + 3i is multiplied by 3, the result is 6 + 9i. Graphically, this shows that the product is a scalar of the complex number.
The correct answer is an option (A)
What is a complex number?"It is number of the form [tex]x+iy[/tex] where the first part (x) is called real part and the second part ([tex]iy[/tex]) is called as imaginary part and [tex]i=\sqrt{-1}[/tex]"
What are real numbers?"It is a combination of rational and irrational numbers, including positive and negative whole numbers, integers, decimals, fractions"
For given example,
The product of a complex number and a real number.
Let, [tex]u[/tex] be any real number and [tex]x+iy[/tex] be any complex number.
The product of 'u' and 'x + iy' is,
[tex]\Rightarrow u\times(x+iy)=(u\times x)+i(u\times y)\\\\\Rightarrow u(x+iy)=ux+i(uy)[/tex]
Let [tex]2+3i[/tex] be a complex number.
For [tex]u=4[/tex],
[tex]\Rightarrow 4\times(2+3i)=8+12i[/tex]
Let [tex]u=-2[/tex],
[tex]\Rightarrow -2\times(2+3i)=-4-6i[/tex]
We can observe that, the product is a scalar of the complex number.
Therefore, when 2+3i is multiplied by 3, the result is 6+9i. Graphically, this shows that the product is a scalar of the complex number.
The correct answer is an option (A)
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Write - 32/12 as a mixed number in reduced form.
Answer: -2 2/3 or -8/3
Step-by-step explanation:
Hope this help
Check all of the correct names for the object pictured below.
A. UT
B. TU
C. UT
D. TU
E. TU
DE UT
8 subtracted by 1/3 + 2/3 equals?
Answer:
8-1/3=7 2/3+2/3=8 1/3
Step-by-step explanation:
I = PRT/100
where
I = simple interest
P = the amount of money invested
R = the interest rate
T = the period of time the money is invested for.
Carla invests £500 for 3 years at a rate of 5%.
How much simple interest does Carla earn?
Answer:
75
Step-by-step explanation:
I = PRT/100
Substitute the values
in
I = 500 * 5 * 3 /100
I = 75
What is the smallest counting number that is divisible by 2, 4, 5, 6, and 12? express each number and your final answer as a product of primes. What do you notice?
Answer:
60
[tex]2^{2} * 3 * 5[/tex]
Step-by-step explanation:
A six sided number cube is rolled. What is the probability of getting a 2 and then a 1, given that the first number rolled was a 2?
Answer:
1/36
Step-by-step explanation:
P(2 then 1) = 1/6 x 1/6 = 1/36
What is excel and how does it work?
Answer:
Excel is a handy software that can be used to store and organize many data sets. Using its features and formulas, you can also use the tool to make sense of your data. For example, you could use a spreadsheet to track data and automatically see sums averages and totals.
Step-by-step explanation:
Go to this website it will answer your question:) The link is below
https://blog.hubspot.com/marketing/how-to-use-excel-tips
select an expression that is equivalent to 4√x2/3
A x14x14
B x94x94
C x16x16
D x83x83
Answer:
here is your answer
Step-by-step explanation:
here is your answer
plsss help !!
Jack and Grace went to the store to buy flowers. Jack bought 3 carnations and 5 roses for a total cost of $22.50. Grace bought 3 carnations and 2 roses for a total cost of $13.50. what does one carnation and one rose cost?
Answer:
carnation $2.50; rose $3.00
Step-by-step explanation:
Let c = price of 1 carnation.
Let r = price of 1 rose.
3c + 5r = 22.5
3c + 2r = 13.50
Subtract the se3cond equation from the first equation.
3r = 9
r = 3
Now substitute r = 3 in the first equation and solve for c.
3c + 5r = 22.5
3c + 5(3) = 22.5
3c = 7.5
c = 2.5
Answer: carnation $2.50; rose $3.00
Which inequality represents the compound in
equality x > 3 and x < 5
Answer:love
Step-by-step explanation:
Inequalities and Absolute Value Equations.
x > 3 and x < 5
Inequality Form:3<x<5
Interval Notation:
(3,5)
An inequality is a mathematical statement that compares algebraic expressions using greater than (>), less than (<), and other inequality symbols
What are the 5 inequalities?The 5 inequality symbols are less than (<), greater than (>), less than or equal (≤), greater than or equal (≥), and the not equal symbol (≠).
Which of the following is an example of compound inequality?Think about the example of the compound inequality: x < 5 and x ≥ −1. The graph of each individual inequality is shown in color. Since the word and joins the two inequalities, the solution is the overlap of the two solutions. This is where both of these statements are true at the same time.
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Solve the inequality for s:
5s + 2 > 7
Answer:
Answer:
S>1
Step-by-step explanation:
5s + 2 > 7
Subtract 2 from both sides
5s>5
Divide 5 from both sides
S>1
Solution of the inequality is s>1.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to one another.
Adding the same amount to each side, taking the same amount away from each side, multiplying or dividing each side by the same positive integer, and other operations can be used to solve the inequality.
The inequality sign must be reversed if either side is multiplied or divided by a negative number.
5s+2 > 7
Subtracting 2 on both side,
5s > 5
s>1
Therefore, the solution set of inequality is s>1.
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Express 384kg in tones
1 kg= 1000 tonnes
384 kg= 384×1000 tonnes = 384000 tonnes
Step-by-step explanation:
384kg = 0.384 tones!!!!!
please help me solve this
Answer:
x=5, y=16
Step-by-step explanation:
y=x^2-9
y=2x+6
solve by substitution
2x+6= x^2 -9
2x+6 = (x+3) (x-3)
2 (x+3) = (x+3) (x-3)
divide both sides by x+3
2= x-3
add 3 to both sides
x=5
y= 2(5) +6
y= 16
Answer:
(-3, 0), (5, 16)Step-by-step explanation:
y = x² - 9y = 2x + 6Solve by substitution:
x² - 9 = 2x + 6x² - 2x - 15 = 0x² - 2x + 1 = 16 (x - 1)² = 4²x - 1 = ± 4x = 1 ± 4x = 5 ⇒ y = 2*5 + 6 = 16x = - 3 ⇒ y = 2*(-3) + 6 = 0X + 2 (x + 1) + 1 in the simplest form
Answer:
3x + 3
Step-by-step explanation:
First, the 2 must be distributed. This leaves us with x + 2x + 2 + 1. x and 2x are like terms, as are 2 and 1. They can be combined, giving us 3x + 3. 3x + 3 cannot be simplified any further, so it is the final answer.
Question: X + 2 (x + 1) + 1 in the simplest form
Answer: 3x+3
ILL GIVE YOU BRAINLIEST IF YOU GET RIGHT AND EXPLAIN
An Angle is half of its supplement.What is the measure of its complement?
Answer:
Step-by-step explanation:
That means that its complement is 90 - 40 = 50 degrees. This also means that its supplement is 180 - 40 = 140 degrees. Therefore, a half of its supplement is 70 degrees and when added to the 50 degree complement the total is 120 degrees, just as the problem said it should be.
==========================================================
Explanation:
Let x be the unknown angle
Its supplement is 180-x, since it must add to x to get 180
The angle x is half of the supplement 180-x, meaning,
x = half of supplement of x
x = half of (180-x)
x = (1/2)*(180-x)
x = 0.5*(180-x)
x = 90 - 0.5x
x+0.5x = 90
1.5x = 90
x = 90/1.5
x = 60
The unknown angle is 60 degrees. It's supplement is 120 because 60+120 = 180, and we can see that 60 is half of 120. So that confirms we have the correct x value.
The last step is to find the complement of angle x. We subtract from 90 like so
90-x = 90 - 60 = 30 which is the final answer
As a check, we can see that 60+30 = 90 to show that we have complementary angles.
------------
Extra info:
It might be easy to mix up the terms "supplementary" and "complementary". What helps me remember is that "supplementary" and "straight angle" both start with S. This could be one way to remember that supplementary angles always add to 180.
Also, both "complementary" and "corner" both start with C, which may be one way to remember that complementary angles always add to 90.
In one season, a basketball player missed 15% of her free throws. How many free throws did she attempt if she made 102 free throws? Write the exact answer. Do not
round
Answer:
120 free throws
Step-by-step explanation:
If she misses 15% of her free throws, that means she makes 85% of them.
Find how many she attempted by dividing 102 by 0.85:
102/0.85
= 120
So, she attempted 120 free throws
The number of free throws that were attempted is 120 free throws.
Since the basketball player missed 15% of her free throws, This means that the percentage scored will be:
= 100% - 15% = 85%
Therefore, 85% of x = 102
0.85x = 102
x = 102/0.85.
x = 120
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Write a linear factorization of the function.
f(x) = x4 + 16x2
f(x) = x2 (4x + i)(4x - i)
f(x) = x2 (x + 4i)2
f(x) = x2 (x + 4i)(x - 4i)
f(x) = x2 (4x + i)2
Answer:
f(x) = x^2 ( x -4i) (x+4i)
Step-by-step explanation:
f(x) = x^4 + 16x^2
Factor out x^2
f(x) = x^2 ( x^2 +16)
f(x) = x^2 ( x^2 - -16)
The square root of -16 is 4i and -4i
Using the difference of square (a^2 - b^2) = (a-b)(a+b)
f(x) = x^2 ( x -4i) (x+4i)
Select the correct systems of equations.
Identify the systems of equations that have A as their point of interest
Answer:
quads
Step-by-step explanation:
convert fraction to decimal 1/8
Answer:
0.125.
Step-by-step explanation:
To convert 1/8 to a decimal, divide the denominator into the numerator. 1 divided by 8 = 0.125.
isn't it .125?
yeah 1/8 is .125 as a decimal
Help me i think it’s c
Answer: Graph B
=====================================================
Explanation:
Point A appears to be at (2.5, -1)
If we shift 6 units to the left, then we subtract 6 from the x coordinate. So the new x coordinate is now 2.5-6 = -3.5
If we shift 4 units up, then we add 4 to the y coordinate to go from -1 to -1+4 = 3
Overall, the point A(2.5, -1) moves to A'(-3.5, 3)
Graph B is the answer because of this. The other points B and C will follow the same pattern as point A does.
finding missing angles 33 33 x
Parrot eats only ........ products
Answer:
Maybe Plants products...
Find the median for the given sample data.
The distances (in miles) driven in the past week by each of a company's sales representatives are listed below.
78 126 238 284 310 356
Find the median distance driven.
A. 261 mi
B. 238 mi.
C. 198.50 mi.
D. 284 mi.
Answer:
d = 261 miles
Step-by-step explanation:
Given that,
The distances (in miles) driven in the past week by each of a company's sales representatives are listed below.
78 126 238 284 310 356
We need to find the median of the distances.
There are 6 data. If n is even,
[tex]median =\dfrac{\dfrac{n}{2}^{th}+(\dfrac{n}{2}+1)^{th}}{2}\\\\median =\dfrac{\dfrac{6}{2}^{th}+(\dfrac{6}{2}+1)^{th}}{2}\\\\=\dfrac{3^{rd}+4^{th}}{2}\\\\=\dfrac{238+284}{2}\\\\=261\ mi[/tex]
So, the median distance is 261 miles.
If f(x) = 3x2 + 1 and g(x) = 1 – x, what is the value of (f – g)(2)?
Answer:
[tex](f-g)(2)=14[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]f(x)=3x^2+1\text{ and } g(x)=1-x[/tex]
And we want to find the value of:
[tex](f-g)(2)[/tex]
This is equivalent to:
[tex](f-g)(2)=f(2)-g(2)[/tex]
Substitute:
[tex]=(3(2)^2+1)-(1-(2))[/tex]
Evaluate:
[tex]=(3(4)+1)-(1-2)=(12+1)-(-1)=13+1=14[/tex]
Therefore:
[tex](f-g)(2)=14[/tex]
