To find g'(a), take the derivative of G(x) with respect to x. Substitute x-values into g'(a) to find slope of tangent line. Use slope and point to write equation of tangent line.
Explanation:To find g'(a), we need to take the derivative of G(x) with respect to x. The derivative of G(x) is the slope of the tangent line to the curve at any given point. In this case, G(x) = x^2 - 7x + 7, so g'(a) = 2a - 7.
For the point (0, 7), we substitute x = 0 into g'(a) to find the slope of the tangent line at that point:
g'(a) = 2(0) - 7 = -7Therefore, the equation of the tangent line at (0, 7) is y = -7x + 7.
Similarly, for the point (6, 1), we substitute x = 6 into g'(a) to find the slope of the tangent line at that point:
g'(a) = 2(6) - 7 = 5Therefore, the equation of the tangent line at (6, 1) is y = 5x - 29.
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Write an equation of the line passing through the point A(2, 0) that is parallel to the line y = 3x−5 .
The equation of the line passing through the point A (2, 0) that is parallel to the line y = 3x - 5 is y = 3x - 6.
To find the equation of a line parallel to the line y = 3x - 5 and passing through point A (2, 0), we can use the fact that parallel lines have the same slope.
The given line has a slope of m = 3. Therefore, any line parallel to it will also have a slope of m = 3.
Now, using the point-slope form of the equation of a line, which is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where m is the slope of the line and [tex](x_1, y_1)[/tex] is a point on the line, we can substitute the values we know:
For point A (2, 0):
[tex]x_1[/tex] = 2
[tex]y_1[/tex] = 0
Slope m = 3
The equation becomes:
y - 0 = 3 (x - 2)
y = 3x - 6
This line has the same slope as the given line, y = 3x - 5, and passes through the point A (2, 0). Therefore, it is parallel to the given line and passes through the given point.
does this table represent a function?why or why not?
x:4,7,8,8,10
y:0,5,5,8,9
What is the midpoint of AB if A = (−2, 2) and B = (3, −1)?
A. (1/2,1/2)
B. (5/2,3/2)
C. (-1/2.-1/2)
D. (-5/2,-3/2)
Find (x - 6)2
a. x2 + 12x + 36
b. x2 - 12x + 36
c. x2 + 6x + 36
s. x2 - 6x + 36
A theater has 500 seats. Three-fourths of the seats are filled. How many seats are filled?
An airplane traveled 1,991.25 kilometers at an average speed of 885 kilometers per hour. How long did it take for the airplane to travel this distance? hours and minutes
Answer:
It took 2 hours and 15 minutes for the airplane to travel 1,991.25 Km
Step-by-step explanation:
In order to find the time, you need to use the fact that average speed = distance traveled/time taken, the problem gives you that the distance traveled is equal to 1,991.25 Km and the average speed is 885 Km/h.
So, you use these values to find the time taken as follows:
[tex]time = \frac{distance}{speed}=\frac{1991.25 km}{885 \frac{km}{h}} = 2.25 h[/tex]
2.25 is a number made by two parts: integer-part and fractional-part.
The integer-part is equal to 2 hours.
The 0.25 is the fractional-part and corresponds to the minutes. 0.25 in fraction is [tex]0.25 = \frac{1}{4}[/tex], the hour has 60 minutes, so when you divided by [tex]\frac{1}{4}[/tex] you the get 15 minutes.
Select all that are like terms to 5a5b4
Answer:
a^5b^4, -a^5b^4, 9a^5b&4
Step-by-step explanation:
Which physical property is shown by scratching one material with another? malleability
viscosity
conductivity
hardness
hardness is the answer for sure
Point A is between points M and C. If MC = 3x+6, find the measure of each segment.
The functions f(x) and g(x) are described below: f(x) = 7x + 9 g(x) = 7x − 4 The graph of g(x) is obtained by shifting down the graph of f(x) by _____ units.
Ms. Harris is stocking up on dry-erase markers for the upcoming school year. She used 56 dry-erase markers last year and plans to use at least that many for next year. The number of markers in each box is two more than three times the number of boxes she purchased for this upcoming school year.
Which of the following inequalities can be used to determine b, the number of boxes she purchased.
Answer:
[tex]3b^2+2b\geq 56[/tex]
Step-by-step explanation:
Here, b represents the number of boxes she purchased for this upcoming school year,
Also, The number of markers in each box is two more than three times the number of boxes she purchased for this upcoming school year.
⇒ The number of marker in each box = 3b+2
Now, the total number of marker = Number of boxes × Number of marker in each box
[tex]=b\times (3b+2)[/tex]
[tex]=3b^2+2b[/tex]
Since, she plan to use at least 56 marker in the upcoming year,
That is, the total number of marker ≥ 56
[tex]\implies 3b^2+2b\geq 56[/tex]
Which is the required inequality that shows the given situation.
Could someone check to see if I'm doing this right please? Will give brainiest. (Picture attached)
Which of the binomials below is a factor of this trinomial? x2 + x - 12
A.x + 4 B.x - 6 C.x - 4 D.x + 6
Answer:A
Step-by-step explanation:
12 is divisble by 4
It costs $3 to bowl a game and $2 for shoe rental. a. Complete the table for the cost of up to 5 games.
You are enclosing a rectangular garden with 60 feet of ornamental fencing. the area of the garden is 200 square feet. what are the dimensions of the garden?
The perimeter is equal to 60 feet and has the formula:
Perimeter = 2 l + 2 w
60 = 2 l + 2 w
The area is equal to 200 square feet and has the formula:
Area = l w
200 = l w
Rewriting area in terms of l:
l = 200 / w
Combining this with the perimeter formula:
60 = 2 (200 / w) + 2 w
60 = 400 / w + 2 w
Multiplying all by w:
60 w = 400 + 2 w^2
Dividing by 2 and rearranging:
w^2 – 30 w = - 200
Completing the square:
(w – 15)^2 = - 200 + (-15)^2
(w – 15)^2 = 25
w – 15 = ±5
w = 10, 20
Hence the dimensions of the garden is 10 feet by 20 feet
The width and length of the rectangular garden, given an area of 200 square feet and a total available perimeter of 60 feet, are 10 feet and 20 feet respectively.
Explanation:To solve this problem, we can use the formula for the area of a rectangle, which is length × width = area, and the perimeter of a rectangle, which is 2(length + width) = perimeter. We know the total perimeter available (which is the ornamental fencing) is 60 feet and the area is 200 square feet.
Let's denote the length of the rectangle as L and the width as W. We can then set up these two equations:
2L + 2W = 60L × W = 200We can simplify the first equation to get L + W = 30 and then isolate either L or W to substitute into the area equation. Let's isolate L to get L = 30 - W.
We then substitute this into the area equation to get: (30 - W)W = 200. Solving this quadratic equation, the possible solutions are W=10 and W=20. However, if W=20, that would leave 0 feet for the length, which is not possible. Therefore, we have W=10 and L=20.
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Use the formula to evaluate the series 3+6+12+24+48+96
What is the solution to the system of equations?
2x – y = 7
y = 2x + 3
(2, 3)
(2, 7)
no solution
infinite number of solutions
Consider
2x – y = 7
y = 2x + 3
Subst. 2x+3 for y in the first equation: 2x - (2x + 3) = 7
This boils down to 0 + 3 = 7, which simply is not true and can never be true.
Thus, this system of equations has no solution.
Answer:
The system of x and y is no solutions.
C is correct
Step-by-step explanation:
Given: System of equation
[tex]2x-y=7[/tex]
[tex]y=2x+3[/tex]
We have system of equation and to solve for x
Using substitution method to solve for x and y
Substitute y=2x+33 into 2x-y=7
[tex]2x-(2x+33)=7[/tex]
[tex]2x-2x-33=7[/tex]
[tex]-33\neq 7[/tex]
-33 is not equal to 7.
We didn't get the value of x.
No solution for x and y
Hence, The system of x and y is no solutions.
Which of the following is the solution set of the given equation?
14 + 8m = 14 - 3m - 5m
A.) Ø
B.) {0}
C.) {all reals}
Use implicit differentiation to find the slope of the tangent line to the curve defined by xy6+6xy=42xy6+6xy=42 at the point (6,1)(6,1).
the slope of the tangent line to the curve at the given point is
Which linear inequality is represented by the graph?
A) y > 2/3x - 2
B) y < 2/3x + 2
C) y > 2/3x + 1
D) y < 2/3x - 1
I NEED THE ANSWER ASAP ‼️
Given: Lines a and b are parallel and line c is a transversal. Prove: 2 is supplementary to 8 What is the missing reason in the proof?
Answer:
your answer is: A
Step-by-step explanation:
corresponding angles theorem.
One nanometer is about 0.00000003937 of an inch. what is this number in scientific notation?
The scientific notation of 0.00000003937 is 3.397 x [tex]10^{-8}[/tex]
what is scientific notation?A given number, equation, or expression is written in a format known as a scientific notation, which adheres to a set of principles. Large numbers like 8.6 billion are difficult to write in their numerical form since they are not only unclear but also time-consuming, and there is a potential that we may write a few zeros more or less. So, we utilise scientific notation to clearly describe extremely large or extremely small integers.
Given number:
0.00000003937
Now, to make the number in standard form we have to write the number in 10 raise to power.
So, 0.00000003937
= 3.397 x [tex]10^{-8}[/tex]
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This graph shows the costs of purchasing two types of laundry detergent.
Which statement is true?
a.) Detergent A is less expensive than Detergent B.
b.) Detergent B is less expensive than Detergent A.
c.) Detergent A and Detergent B cost about the same.
Answer:
the other person is correct
Step-by-step explanation:
A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid. T. A. =
Answer:
[tex](24\sqrt{3}+72)\text{ square unit}[/tex]
Step-by-step explanation:
Since, the area of a regular hexagon is,
[tex]A=\frac{3\sqrt{3}}{2}a^2[/tex]
Where, a is the side of the hexagon,
Here, the base of the pyramid is a regular hexagon having side length,
a = 4 unit,
Thus, the base area of the pyramid is,
[tex]A_B=\frac{3\sqrt{3}}{2}(4)^2[/tex]
[tex]=\frac{48\sqrt{3}}{2}[/tex]
[tex]=24\sqrt{3}\text{ square unit}[/tex]
Now, the lateral face of the pyramid is a triangle having base = 4 unit and height = 6 unit,
Also, a hexagonal pyramid has 6 triangular faces,
So, the total lateral area of the pyramid is,
[tex]A_L=6\times \frac{1}{2}\times 4\times 6[/tex]
[tex]=\frac{144}{2}[/tex]
[tex]=72\text{ square unit}[/tex]
Hence, the total area of the pyramid is,
[tex]T.A.=A_B+A_L[/tex]
[tex]=(24\sqrt{3}+72)\text{ square unit}[/tex]
Answer:
[tex]24\sqrt3+72[/tex] Square units
Step-by-step explanation:
We are given that a pyramid which has a regular hexagonal base.
Side length of hexagonal base=Base of triangular face=4 units
Height of triangle=6 units
We have to find total area of the pyramid.
The total area of pyramid=[tex]A_B+A_L[/tex]
Where [tex]A_B[/tex]=Base area
[tex]A_L[/tex]=Lateral area
Area of hexagonal base=[tex]\frac{3\sqrt3}{2}a^2[/tex]
Where a= Side length
Now, area of hexagonal base=[tex]\frac{3\sqrt3}{2}(4)^2=24\sqrt3[/tex] square units
Area of triangular face=[tex]\frac{1}{2}\times base\times height=\frac{1}{2}\times 6\times 4=12[/tex] square units
In pyramid , there are 6 triangular faces.
Therefore, lateral area of pyramid=[tex]6\times 12=72[/tex] square units
Substitute the values in the given formula then, we get
Total lateral area of given pyramid=[tex]24\sqrt3+72[/tex] Square units
What is the intersection of planes ADE and BEA?
a.) Plane BED
b.) Plane ABC
c.) Line BD
d.) Line AE
Answer:
d.) Line AE
Step-by-step explanation:
We have been given a diagram. We are asked to find the intersection of planes ADE and BEA.
Upon looking at our given diagram, we can see that both planes intersect only at two points that are point A and E respectively.
We can also see that the line AE is a common side of both planes, therefore, line AE is the intersection of planes ADE and BEA.
Find the common difference for the sequence shown 1/4,5/16,3/8
A wise man once said “200 reduced by twice my age is 42” What is his age ?
Some of the steps in the derivation of the quadratic formula are shown. Step 4: Step 5: Step 6: Step 7: Which best explains why the expression cannot be rewritten as during the next step? Negative values, like −4ac, do not have a square root. The ± symbol prevents the square root from being evaluated. The square root of terms separated by addition and subtraction cannot be calculated individually. The entire term b2 − 4ac must be divided by 2a before its square root can be determined.
Answer:c
Step-by-step explanation:
The answer is the square root of terms separated by addition and subtraction cannot be calculated individually.
To find expression cannot be rewritten as during the next step and explain.
What is expression?Algebraic expressions are combinations of variables , numbers, and at least one arithmetic operation.
The statement that best explains why the expression cannot be rewritten as during the next step is that the square root of terms separated by addition and subtraction cannot be calculated individually.
So, the square root of terms separated by addition and subtraction cannot be calculated individually.
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Four doughnuts and 4 coffees cost $12. The cost of the 4 coffees is half the cost of the 4 doughnuts. What is the cost of each coffee?
A cashier always starts the day with $60 in pennies, nickels, dimes, and quarters. She begins with five times as many pennies as quarters, and the number of nickels and dimes are both twice the number of quarters. How many pennies does she start with?
6 pennies
26 pennies
100 pennies
500 pennies