The gradient of the function at the point (-1 -7) is 3a - 6.
What is the gradient of the function?
A function's gradient is also known as its slope, and the slope (of a tangent) at a given point on a function is known as its derivative.
We have,
g(x) = ax³ + 3x² + bx + c
Take the derivative of the function with respect to x, then substitute the x-coordinate of the point of interest in for the x values in the derivative to find the gradient.
to know the gradient of the function ax³ + 3x² + bx + c at the point (-1, -7) we would do the following:
Take the derivative with respect to x:
g'(x) = 3ax² + 6x + b
Substitute the x-coordinate (x = -1)in for x:
gradient = 3a(-1)² + 6(-1) + b = 3a - 6
So the gradient of the function at the point (-1 -7) is 3a - 6.
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SCHOOL Antonio earned these scores on the first three tests in history this term: 89, 92, and 81. What is the lowest score that Antonio can earn on the fourth and final test of the term if he wants to have an average of at least 87?
Answer:
86
Step-by-step explanation: 89+92+81+x=total score=262+x
avg score = 87= (262+x)/4
262+x=348
.
x=86
.
Check,,,(89,92,81,86)/4 = 87
Answer: 86
Step-by-step explanation:
from the package. What fraction shows what part of the package they have eaten? Sofia's family buys little boxes of cereal in a package containing 10 boxes. They have eaten 6 boxes of cereal from the package.What f fraction shows what part of the packages they have eaten .
The fraction which shows what part of packages they have eaten is 3/5.
What is fraction?
A fraction is characterized as a portion of something larger. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers.
Main Body:
Total no. of boxes of cereals in a package = 10
Total no. of boxes eaten by family = 6
Fraction can be calculated by directly by diving the values.
Fraction ⇒ 6/10
dividing by 2 on both denominator and numerator
hence, Simple fraction is 3/5.
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The hour hand of a clock moves −30° every hour. How many degrees does it move in 2 1/5 hours? The hour hand of a clock moves ______ ° in 2 1/5 hours.
The number of degrees does it move in 2 1/5 hours is -66°.
How to calculate the number of degrees?From the information given, it was illustrated that the hour hand of a clock moves −30° every hour.
Therefore, to calculate the degree for a number of hours, we simply have to multiply.
In this case, to get the degree for 2 1/5 hours will be:
= Degree every hour × Number of hours
= -30° × 2 1/5
= -30° × 2.2
= -66°
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When the mortgage is completely paid off for Mark and Lynne’s house, it will be 5 times as old as it is now. If they have 20 years left on the mortgage, how old is the house right now?
The age of Mark and Lynne’s house right now, given the number of years left till the mortgage is paid off is 4 years.
How to find the age of the house?Mark and Lynne’s house is currently aged such that in 20 years when the mortgage is paid off, it will be five times as old as it is now.
Assuming the age of the house right now is x, the age of the house can be shown in an equation as:
20 years = 5x
The age of the house now is therefore:
x = 20 / 5
x = 4 years
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The ratio of girls to boys in the school is 3 to 1. If there is a total of 400 students, how many are boys? The answer must be a whole number.
Step-by-step explanation:
girls:boys
3:1
total=400
1/3 × 400
400/3
=133.33
to whole number
=133 boys
Answer:
The correct answer is 100
Kevin needs to read 3 novels each month.
Let N be the number of novels Kevin needs to read in M months.
Write an equation relating N to M. Then use this equation to find the number of novels Kevin needs to read in 19 months.
Kevin needs to read 57 novels in 19 months.
Given,
The number of novels Kevin needs to read in a month = 3
N = Number of novels Kevin needs to read in M months.
Write an equation with M and N.
That is,
Kevin needs to read 3 novels in one month.
So, number of novels, N Kevin reads in M months, 3M = N
The equation is;
3M = N
Now,
The number of months Kevin needs to read the novels = 19
Then,
The number of novels Kevin reads in 19 months;
3M = N
3 × 19 = 57
That is,
Kevin needs to read 57 novels in 19 months.
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Solve the equation 42 = v + 35 for v.
A. −77
B. 77
C. −7
D. 7
Answer:
v = 7
Step-by-step explanation:
42 = v + 35
-35 -35
7 = v
The answer is D. 7
I took the quiz and got it right
20. To calculate your electric bill for your home, DTE uses the following equation: C = 5 + 4e where C is how much they charge you and e is the amount of electricity used measured in kilowatt-hours (kwh) used.
a. Does this situation represent a linear function? Explain.
b. Find the domain of the function. Is the domain discrete or continuous? Explain.
c. Graph the function using its domain.
Considering the function C = 5 + 4e, it is found that:
a. The situation represents a linear function, as the increase in the price is constant for each kwh hour used.
b. The continuous domain of the function is: e ≥ 0.
c. The graph of the function is given by the image shown at the end of the answer.
What is a linear function?A linear equation is a special function that has the format of the equation given as follows:
y = mx + b.
The coefficients of the equation y = mx + b are given as follows:
m is the slope, representing the rate of change of y relative to x.b is the y-intercept, representing the value of y when x = 0.For this problem, the function is:
C(e) = 5 + 4e.
Which is a linear function, as it follows the same format of the general linear function, with a constant cost of 4 per each kwh used.
The domain of the function contains the set of all possible input values of the function. Hence, in this problem, it is composed by the amounts of kwh used, which:
Is a continuous amount, as it can assume decimal values.Cannot assume decimal values.Hence the domain is:
e ≥ 0.
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Bro please help. Im so lost
Answer:
D: x≤-4
Step-by-step explanation:
If its not just reply to me and i will re asses
Answer:
3
Step-by-step explanation:
Solve ex = e2x + 5. Answers: A.) x = 10 B.) x = -5 C.) x = 5 D.) x = -2
The value of ex = e2x + 5 is -5.
What is mean by exponential function ?The mathematical expression f(x)=exp or ex denotes the exponential function. Unless otherwise stated, the term typically refers to the positive-valued function of a real variable. it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
A mathematical function with the formula f (x) = an x is an exponential function. where an is a constant known as the function's base and x is a variable. The transcendental number e, or roughly 2.71828, is the exponential-function base that is most frequently encountered.
Given ,
[tex]e^x=e^{2 x}+5[/tex]
By simplifying the exponential rule we get
x= -5
Therefore the value of [tex]e^x=e^{2 x}+5[/tex] is -5
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7 is what percent of 77? please with work!!!
Answer:
5.39
Step-by-step explanation:
Answer: 9.09%
that is the answer
A bicycle wheel has diameter 66 cm. Find how many turns the wheel makes when the bicycle travels 400 metres.
The number of turns the wheel makes is 1.93 ≈ 2.
What is Turns?
This is referred to as a cycle. It is a unit of plane angle measurement that is equivalent to 2π radians, 360 degrees, or 400 gradians.
formular for calculating Turns:
Turns = Lenght
Circumference
Circumference of a circle, C= πD
Where,
Diameter=D
π =22/7
Calculating Circumference;
C= 22 * 66
7
=207.4
From the question:
D= 66cm
L =400m
Calculating Turns:
Turns = Lenght
Circumference
= 400m
207.4
Turns =1.93
Turns =1.93≈ 2
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-8(1+4p) +7p =-25-8p
Answer:
p = 1
Step-by-step explanation:
Given equation,
→ -8(1 + 4p) + 7p = -25 - 8p
Let's solve for the value of p,
→ -8(1 + 4p) + 7p = -25 - 8p
→ -8 - 32p + 7p = -25 - 8p
→ -32p + 7p + 8p = -25 + 8
→ -17p = -17
→ p = (-17)/(-17)
→ [ p = 1 ]
Hence, the value of p is 1.
Jorani buys [tex]8\frac{1}{3}[/tex] bolts of fabric. Each bolt has 24m of fabric. The fabric costs $1.65/m. Determine the total cost of the fabric.
The total cost of the fabric Jorani bought is 330 dollars.
How to find the total cost of the fabric?Jorani buys [tex]8\frac{1}{3}[/tex] bolts of fabrics. Each bolt has 24m of fabric. The fabric costs $1.65 per metres. The total cost of the fabric can be calculated as follows:
1 bolt = 24 metres
25 / 3 bolt = ?
cross multiply
length of the fabrics = 25 / 3 × 24
length of the fabrics = 600 / 3
length of the fabrics = 200 metres
Therefore,
1 metres = 1.65 dollars
200 metres = ?
cross multiply
cost of the fabric = 200 × 1.65
cost of the fabric = 330 dollars
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!
The solution is
1) Angles 7 and 6 are Vertical angles
2) Angles 1 and 8 are Alternate exterior angles
3) Angles 4 and 5 are Alternate interior angles
4) Angles 2 and 6 are Corresponding angles
5) Angles 6 and 8 are Complementary angles
What are angles in parallel lines?
Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.
We can conclude three factors determining parallel lines ,
Alternate angles are equalCorresponding angles are equalCo-interior angles add up to 180°Given data ,
Alternate angles are angles that occur on opposite sides of the transversal line and have the same size.
Each pair of alternate angles around the transversal are equal to each other.
The pairs of angles formed on the same side of the transversal that are either both obtuse or both acute and are called corresponding angles and are equal in size.
Each pair of corresponding angles on the same side of the intersecting transversal are equal to each other.
Co-interior angles on the same side of an intersecting transversal add to 180°
Hence , the angles are
1) Angles 7 and 6 are Vertical angles
2) Angles 1 and 8 are Alternate exterior angles
3) Angles 4 and 5 are Alternate interior angles
4) Angles 2 and 6 are Corresponding angles
5) Angles 6 and 8 are Complementary angles
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Jermaine plots the point (0,0)and (4,11) on a graph to represent a proportional relationship. Which of the following equation represents the relationship between the x and y values
A)y=4 x. b)y=2.75x c)y=0.36x d)11y=4x
-----
11
The equation represents the relationship between the x and y values is y = 2.75x
The first point = (0,0)
The second point = (4,11)
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line m = (11-0) / (4-0)
= 11 / 4
= 2.75
The slope intercept form is
y = mx + b
m is the slope of the line
b is the y intercept
The equation will be
y = 2.75x
Hence, the equation represents the relationship between the x and y values is y = 2.75x
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A trainer devised a 40 minute workout plan for client. The table shows the number of minutes spent on each type of exercise.
TABLE:
Endurance:8
Strength:16
Balance:4
Flexibility:12
The grid has 100 squares and each exercise will be represented by the following percentages:
Endurance = 20% (20 squares)Strength = 40% (40 squares)Balance = 10% (10 squares)Flexibility = 30% (30 squares).What are percentages?Percentages refer to the ratio or proportion of a value when compared to the whole.
Percentages are fractional values, computed as a quotient of the part with respect to the whole, and usually expressed over 100.
The percentage sign (%) is used to depict values in percentages.
TABLEExercise Minutes Percentage
Endurance: 8 20% (8/40 x 100)
Strength: 16 40% (16/40 x 100)
Balance: 4 10% (4/40 x 100)
Flexibility: 12 20% (12/40 x 100)
Total 40 100% (40/40 x 100)
Thus, the percentage representation of the exercises on the grid shows that Endurance occupies 20%, Strength 40%, Balance 10%, and Flexibility 30%.
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Question Completion:In the grid below, represent the percentage of each exercise.
Mindy owns 20 pairs of shoes and every week he purchases two more but destroys one. How long will it take for her closet to have 50 pairs of shoes.
Solve and write an equation.
Answer:
29 weeks---------------------
Initial number of pairs of shoes is 20.
To achieve 50 pairs Mindy needs 30 more pairs.
Each week 2 pairs added but 1 removed. It makes total of 1 pairs addition.
After 28 weeks Mindy will have 20 + 28 = 48 pairs of shoes.
The next week he will purchase 2 more pairs and get 50 pairs in total.
The number of weeks it will take for her closet to have 50 pairs of shoes would be = 30 weeks.
What is purchase price?A purchase price is the amount of money that was use to obtain a valuable.
The number of shoes owned by Mindy = 20 pairs
The number of shoes Mindy purchases per week = 2 pairs
The number of shoes Mindy destroys = 1 pair.
Therefore, in a week Mindy has an additional 1 pair of shoe.
The number of pairs she needs extra = 50-20 = 30
Since 1 pair of shoe = 1 week, she will require 30 weeks to purchase additional 30 pairs making it up to 50 pairs of shoes she owns.
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Increase £16470.45 by 3.5%
Give your answer rounded to 2 DP
Answer:
it is £16490.36
Step-by-step explanation:
since £156.78 is 100%, £16470.45 by 3.5 is £16490.36
Answer:
it's 17,046.92
Step-by-step explanation:
that's what my calculations said
When a number is decreased by 53%, the result is 30
Explain how you found your answer.
Answer: First, I substituted x for 11. -2 times 11 = -22. -22 + 5 equals -17. Therefore, f(11) or y, is equal to -17.
Step-by-step explanation:
Part A: Timothy said that AKLM was dilated by a scale factor of 1.5 centered at the origin. Is Timothy CORRECT? Explain your answer or show your work.
Yes Timothy is correct because triangle AKLM was dilated by a scale factor of 1.5 centered at the origin.
What is dilation?In Geometry, dilation simply refers to a type of transformation which changes the size of a geometric object based on the scale factor, but not its shape.
For the given vertices of triangle KLM, the dilation with a scale factor of 1.5 from the origin (0, 0) or center of dilation should be calculated as follows:
Point K (-1, 3) → Point K' (-1 × 1.5, 3 × 1.5) = Point K' (-1.5, 4.5).
Point L (8, 4) → Point L' (8 × 1.5, 4 × 1.5) = Point L' (12, 6).
Point M (10, -3) → Point M' (10 × 1.5, -3 × 1.5) = Point M' (15, -4.5).
In conclusion, the coordinates of the image triangle K'L'M after a dilation with a scale factor of 1.5 from the origin are (-1.5, 4.5), (12, 6), and (15, -4.5) as shown in the graph, and as such Timothy is correct.
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write the equation of a line that is parallel to y=1/2x+4 and goes thru the point(-3,4)
The standard form equation for a line passing through the point (-3, 4) and parallel to the line denoted by y = 1/2x+4 is 2y - x = 11.
The standard form equation
ax + by = c
Here a, b, and c are constants and therefore use the slope-intercept form.
y = mx + c ...... (1)
where m is the slope, b = y-intercept
y = 1/2x + 4
Slope (m) = 1/2
It passes through a line that has points (-3,4)
Let's find c by putting the value of x = -3 and y = 4 in equation (1).
4 = 1/2 (-3) + c
4 = -3/2 + c
c = 4 + 3/2
=> c = (8+3)/2
=> c = 11/2
Therefore,
y = 1/2x + 11/2
y = (x+11)/2
=> 2y - x = 11
2y - x = 11 is the standard form of the line that passes through (-3,4) and is parallel to the line represented by y = 1/2x+4.
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What value is needed to complete the square? Show all steps.
x^2 - 2x +__
In completing the square method, considering the equation X^2 - 2x + the number to be added should be 1 to make it a perfect square
How to know term that should addedThe standard quadratic equation is of the form
ax^2 + bx + c
The completing the square method is one of the methods of solving quadratic equations
The factor to be added to the equation while using the completing the square method is of the formula
(b / 2a)^2
compared to the equation in the problem X^2 - 2x +
= (b / 2a)^2
= (2 / 2)^2
= (1)^2
= 1
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Which is a Fibonacci number?
189
7
233
6
Answer:
233 is a Fibonacci number
Step-by-step explanation:
The Gallup Poll reported that 48% of Americans spend more than an hour a day using the Internet. If 6 people are selected at random, find the probability that they all spend more than an hour a day using the Internet. Please round the final answer to 2 or 3 decimal places.
Answer:
the answer is that there is 8 percent that they all will spend an hour on the internet.
Step-by-step explanation:
Identify the graph of the equation of the form y=ax²+bx+c with a<0 and having two x-intercepts.
Choose the correct answer below.
E B
D A
C F
In the graphs given, only graph F has two x - intercepts and a < 0 i.e the graph is facing downwards or opens downwards
Graph of Quadratic FunctionThe graph of a quadratic function is called a parabola and has a curved shape. One of the main points of a parabola is its vertex. It is the highest or the lowest point on its graph. You can think of like an endpoint of a parabola.
In this question, we have to find the graph of a function f(x) that a < 0 and has two intercepts.
The easy features of this graph are
The graph must touch two opposite side on the x-axisThe graph must be facing downwardsIn the options given, only graph F has such features and it is the answer to the question.
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PLEASE HELP find the measure of each marked angle
Step-by-step explanation:
When dealing with transversals, most angles either add to 180 or equal to each other. These angles form a linear pair so they add to 180
[tex](x + 1) + 4x - 36 = 180[/tex]
[tex]5x - 35 = 180[/tex]
[tex]5x = 215[/tex]
[tex]x = 43[/tex]
So
[tex]x + 1 = 43+ 1 = 44[/tex]
[tex]4(43) - 36 = 136[/tex]
Answer:
x + 1 = 44 degrees
4x - 36 = 136 degrees
Step-by-step explanation:
Since the lines are parallel, the angles are same-side-interior angles, which means they are supplementary and add up to 180:
x + 1 + 4x - 36 = 180
5x - 35 = 180
5x = 180 + 35
5x = 215
x = 43
x + 1 = 43 + 1 = 44 degrees
4x - 36 = 4(43) - 36 = 136 degrees
Really quick! Need help...and will give brainliest to the first correct answer.
Answer:
[tex]x + 3y = -30:[/tex] Perpendicular to line a
[tex]y = \frac{1}{3} x + 1 :[/tex] Neither Parallel nor Perpendicular to line a
[tex]-3x + y = -2 :[/tex] Parallel to line a
Explanation:
[tex]-3x + y = -4\\y = 3x - 4[/tex]
[tex]x + 3y = -30\\3y = x - 30\\y = \frac{1}{3} x - 10[/tex]
[tex]y = \frac{1}{3} x + 1[/tex]
[tex]-3x + y = -2\\y = 3x - 2[/tex]
A group of 16 people is choosing a chairperson and vice-chairperson. They put all 16 people's names into a hat. The first name drawn becomes chair. The second name drawn becomes vice-chair. How many possible combinations of chair and vice-chair are there?
Answer: 240 combinations
Step-by-step explanation: So basically because you can have a possibility of 16 people being chairperson and 15 vice chairpersons, so all you have to do is multiple 16x15 which is 240.
