The line tangent to g(x) at x = 3 is:
y = 4*x - 18
How to find the equation of the tangent line?
If we have a function y = f(x), the slope of the line tangent at the point x = a is given by f'(a).
In this case, we know that g'(3) = 4, so the slope of the line is 4.
Then the line is something like:
y = 4*x + b
To find the value of b we use the fact that this line must pass through the point (3, g(3))
And we know that g(3) = -6
Then this line must pass through the point (3, -6), replacing that we get:
-6 = 4*3 + b
-6 = 12 + b
-6 - 12 = b = -18
Then the tangent line is:
y = 4*x - 18
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What fraction is equivalent to the expression
21
16
÷
7
4
?
Answer:
3/4
Step-by-step explanation:
21/16 ÷ 7/4
21/16 × 4/7
3/4
Evaluate the function rule for the given value. y = 12 • 3^-2 for x = –2
I need help with this one
Answer:
that's your answer
Determine the intercepts of the line.
x-intercept ( , )
y-intercept ( , )
Answer:
y-100
x-250
Step-by-step explanation:
because the lines are insecting the other lines on that line
I can write linear equations
1. Through: (-1,3), Slope=2
2.Through: (3,3), slope= -2
Help? Will give brainliest!
Answer:
Top one
Step-by-step explanation:
It is more appropriate to measure the speck of dust using millimeters because that is most similar to the scale of the speck's size.
I can't seem to figure this one out. Could someone show how to do it and the answer? Thanks in advance!
Answer:
[tex]\displaystyle (-\infty, -\frac{1}{6})[/tex]
Step-by-Step explanation:
We have the function:
[tex]\displaystyle y=\int_{1}^{x}\frac{1}{3+t+3t^2}\, dt[/tex]
And we want to find the interval for which y is concave upwards.
Therefore, we will need to find the second derivative of y, find its inflection points (where y''=0), and test for values.
So, let's take the derivative of both sides with respect to x. So:
[tex]\displaystyle y^\prime=\frac{d}{dx}\Bigg[\int_{1}^{x}\frac{1}{3+t+3t^2}\, dt\Bigg][/tex]
By the Fundamental Theorem of Calculus:
[tex]\displaystyle y^\prime=\frac{1}{3+x+3x^2}[/tex]
So, we will take the derivative again. Hence:
[tex]\displaystyle y^\prime^\prime=\frac{d}{dx}\Big[\frac{1}{3+x+3x^2}\Big]=\frac{d}{dx}\Big[(3+x+3x^2)^{-1}\Big][/tex]
We will use the chain rule. Let:
[tex]\displaystyle u=x^{-1}\text{ and } v=3+x+3x^2[/tex]
Differentiate:
[tex]\displaystyle y^\prime^\prime=-(3+x+3x^2)^{-2}(1+6x)[/tex]
Rewrite:
[tex]\displaystyle y^\prime^\prime=-\frac{6x+1}{(3+x+3x^2)^2}[/tex]
So, points of inflection, where the concavity changes, is whenever the second derivative is 0 or undefined.
We can see that the second derivative will never be undefined since the denominator can never equal 0.
So, our only possible inflection points are when it's equal to 0. Hence:
[tex]\displaystyle 0=-\frac{6x+1}{(3+x+3x^2)^2}[/tex]
Multiplying both sides by the denominator gives:
[tex]0=-(6x+1)[/tex]
Then it follows that:
[tex]\displaystyle x=-\frac{1}{6}[/tex]
So, our only possible point of inflection is at x=-1/6.
We will test for values less than and greater than this inflection point.
Testing for x=-1, we see that:
[tex]\displaystyle y^\prime^\prime=-\frac{6(-1)+1}{3+(-1)+3(-1)^2}=1>0[/tex]
Since the result is positive, y is concave up for all values less than -1/6.
And testing for x=0, we see that:
[tex]\displaystyle y^\prime^\prime=-\frac{6(0)+1}{3+(0)+3(0)^2}=-\frac{1}{3}[/tex]
Since the result is negative, y is concave down for all values greater than -1/6.
Therefore, the interval for which y is concave up is:
[tex]\displaystyle (-\infty, -\frac{1}{6})[/tex]
Note that we use parentheses instead of brackets since at exactly x=-1/6, our graph is neither concave up nor concave down.
Solve the equation below by factoring, then select ALL of the possible solutions.
f (x) = x^2 - 9x - 36
a . x = - 12
b. x = - 9
c. x = - 6
d. x = - 4
e. x = - 3
f. x = - 2
g. x = 2
h. x = 3
i. x = 4
j. x = 6
k. x = 9
l. x = 12
giving brainliest !!!!
Answer:
It is A or D but mostly A is correct.
Step-by-step explanation:
give brainliest
9-3x/9=-11 what is x and how you did it in a way that isn’t complicated please
The value of a baseball player's rookie card began to increase once the player retired. When he retired in 1999 his card was worth $4.99. The value has increased by $1.73 each year since then. Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y proportional? What was the value of the card in 2006? Express the relationship with an equation. y=(Use integers or decimals for any numbers in the expression.)
Answer: $15.37
Yes, proportional
Step-by-step explanation:
Ok So the Equation Here is
y = 1.73x + 4.99
The reason why 4.99 doesn't have a variable is because of the fact it's not being manipulated by time like the 1.73 is. It's a flat rate of 4.99 for the card itself, no increase or decrease in years. However, the 1.73 is affected by how ever many years the player is in retirement. That's why it has X because the amount of 1.73 needs to be multiplied by however many years hes been in retirement.
So Substitute 6 (because 2006 is what year we need to find) for x and we get
y = 1.73(6) + 4.99
Which if you simplify in a calculator or do it in your paper, comes out to be $15.37
*If this Helped I'd Also Appreciate 5* and a ♥ Thanks!*
The cube of the product of 8 and a number.
The unknown number will be equal to 64.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the cube of the product of 8 and the number is 512. The unknown number will be calculated as,
8 x = 512
x = 512 / 8
x = 64
The number which is the product of 8 will be equal to 64.
The complete question is given below.
The cube of the product of 8 and the number is 512. What is the number?
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13 more than x times 5 as an expression
Answer: I believe it's 13 > 5x or 5x+13. . But I'm not completely sure.
Evaluate 1/8 + 3/4 Fhffh
Answer:
7/8
Step-by-step explanation:
1/8 + 3/4 =
1/8 + 6/8 =
7/8
Please help me with my question
Answer: use mahthway it hels
Step-by-step explanation:
The average daily maximum temperature in Syracuse is 21.85°C, and the average daily minimum temperature is -4.7°C. The average daily maximum temperature is BLANK °C higher than the average daily minimum temperature.
Answer:
The average daily maximum temperature is
26.56 °C higher than the average daily minimum temperature
Step-by-step explanation:
Here, we simply want to calculate how higher is the average daily maximum temperature to average daily minimum temperature
We simply proceed to subtract the two
Mathematically, that will be;
21.85 - (-4.7)
= 21.85 + 4.7
= 26.56 °C
how is 1/14x42=3 can someone? explain
Answer:
This is why [tex]\frac{1}{14}[/tex] x 42 = 3
Step-by-step explanation:
[tex]\frac{1}{14}[/tex] x 42 can also be written as [tex]\frac{1}{14}[/tex] x [tex]\frac{42}{1}[/tex]
we can reduce diagonally by 7 so [tex]\frac{1}{14}[/tex] x [tex]\frac{42}{1}[/tex] = [tex]\frac{1}{2}[/tex] x [tex]\frac{6}{1}[/tex]
now we multiply across [tex]\frac{1}{2}[/tex] x [tex]\frac{6}{1}[/tex] = [tex]\frac{6}{2}[/tex]
6 divided by two or [tex]\frac{6}{2}[/tex] = [tex]\frac{3}{1}[/tex] or 3
PLEASE HELP ME!!!!! WILL GIVE BRAINLIESTTTTTTTTTT!!!!!!!
Answer:
Domain: -3 ≤ x ≤ 3
Range: -2 ≤ y ≤ 4
General Formulas and Concepts:
Algebra I
Domain is the set of x-values that can be inputted into function f(x) Range is the set of y-values that are outputted by function f(x)Step-by-step explanation:
According to the graph, our x-values span from -3 to 3. Since both are closed dot, they are inclusive in the domain:
[-3, 3] or -3 ≤ x ≤ 3
According to the graph, our y-values span from -2 to 4. Since both are closed dot, they are inclusive in the range:
[-2, 4] or -2 ≤ y ≤ 4
Anna's favorite pool toys are the beach balls. If the radius of one of the beach balls
is 6 inches, to the nearest whole number, what is the volume of the beach ball?
Leave your answer in terms of a.
Inches Cubed
Answer:
288
Step-by-step explanation:
please review the attachment for step by step soluation
Two numbers are in the ratio 2:5 .If their sum is 28 ,find the numbers
Answer:
8:20
Step-by-step explanation:
8+20=28 and all that has happened is the ratio got bigger.
Suppose a and b are positive integers such that lcm(a,b) = 90 and gcd(a,b) = 3. If b is three more than a, then what are the values of a and b?
Given:
LCM(a,b) = 90 and GCD(a,b) = 3.
b is three more than a.
To find:
The values of a and b.
Solution:
We have,
LCM(a,b) = 90
GCD(a,b) = HCF(a,b) = 3
According to the question,
[tex]b=a+3[/tex]
If a and b are two positive integers, then
[tex]a\times b=HCF(a,b)\times LCM(a,b)[/tex]
[tex]a\times (a+3)=3\times 90[/tex]
[tex]a^2+3a=270[/tex]
[tex]a^2+3a-270=0[/tex]
Splitting the middle terms, we get
[tex]a^2+18a-15a-270=0[/tex]
[tex]a(a+18)-15(a+18)=0[/tex]
[tex](a+18)(a-15)=0[/tex]
Using zero product property, we get
[tex]a+18=0[/tex] and [tex]a-15=0[/tex]
[tex]a=-18[/tex] and [tex]a=15[/tex]
a is a positive integer so it cannot be negative. So, a=15.
Now,
[tex]b=a+3[/tex]
[tex]b=15+3[/tex]
[tex]b=18[/tex]
Therefore, the value of a is 15 and the value of b is 18.
Let f(x) = 2x^2-2x+ 7 and g(x) = x^2 + 9x -6z Find f(x) - g(x).
A. X^2-11x+13
B. X^2-11x+1
C. X^2+7x+1
D. X^2+7x+13
Heres the answer welcome btw
2x<6 solve the following inequality
Answer:
x<3
Step-by-step explanation:
2x<6
/ /
2 2
x<3
Need this ASAP thanks
Answer:
In Step 2.
Step-by-step explanation:
They should have distributed the 2 to the x and 1 instead of subtracting it.
Which graph represents an even function?
Answer:
one that looks like triangle
Step-by-step explanation:
1. If 5 lbs of apples cost $2.99, How much would 3 lbs cost?
Solve the equatuon
x/2-(2/(x+1))=1
x=?
[tex]\frac{x}{2}-\frac{2}{x+1}=1[/tex]
We have 2 denominators that we need to get rid of. Whenever there are the denominators, all we have to do is multiply all whole equation with the denominators.
Our denominators are both 2 and x+1. Therefore, we multiply the whole equation by 2(x+1)
[tex]\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)][/tex]
Then shorten the fractions.
[tex]\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)]\\x(x+1)-2(2)=1(2x+2)[/tex]
Distribute in all.
[tex]x^2+x-4=2x+2[/tex]
We should get like this. Because the polynomial is 2-degree, I'd suggest you to move all terms to one place. Therefore, moving 2x+2 to another side and subtract.
[tex]x^2+x-4-2x-2=0\\x^2-x-6=0\\[/tex]
We are almost there. All we have to do is, solving for x by factoring. (Although there are more than just factoring but factoring this polynomial is faster.)
[tex](x-3)(x+2)=0\\x=3,-2[/tex]
Thus, the answer is x = 3, -2
-60+x-23=70
Need help
Answer:
x-83=70
x = 70 + 83
x= 153
What is the volume of a cylinder, in cubic ft, with a height of 9ft and a base diameter
of 16ft? Round to the nearest tenths place
Answer:
Volume of cylinder is: Volume=1808.64 ft³
Step-by-step explanation:
Height of cylinder = 9 ft
Base diameter of cylinder = 16 ft
We need to find volume of cylinder .
The formula used is: [tex]Volume=\pi r^2h[/tex]
We need radius:
The radius = diameter/2 = 16/2 = 8 ft
Putting values and finding volume of cylinder
[tex]Volume=\pi r^2h[/tex]
[tex]Volume=3.14\times (8)^2\times (9) \\Volume=3.14\times 64\times (9) \\Volume=1808.64 \: ft^3[/tex]
So, Volume of cylinder is: Volume=1808.64 ft³
question is in the picture.
Answer: About 16 snaps
Step-by-step explanation:
In a box and whisker plot, the rightmost line in the "box" of the plot is the third quartile, which represents the 75th percentile.
In this graph, although it is difficult to pinpoint the EXACT number of snaps sent, the 75th percentile would be marked at about 16 snaps.