The only statement that is true as regards the graph of f ′(x) is;
C: f is decreasing on the interval from x = 1 to x = 2
We are told that the graph of f ′(x) has x-intercepts at x = –3, x = 1 and x = 2.Now, f'(x) is simply the derivative of f(x) and the derivative of f(x) is defined as the slope.
Since x-intercepts of the derivative are at x = –3, x = 1 and x = 2. It means that the values of x that will make the slope to be zero are x = –3, x = 1 and x = 2.Now, the minimum for the derivative graph usually happens when the the graph goes from negative to positive. This means that the graph is decreasing when the x-intercepts of the slope is positiveIn contrast the graph is increasing when the x-intercepts of the slope is negative.
Let us look at the options;
Option A; This is not correct because the derivative has to be zero at minimum point. Option B; This is not also correct because the derivative has to be zero at maximum point.Option C; This is correct because slope is positive when the graph is decreasing and from x = 1 to x = 2 is positive interval.Read more about graph of derivative of a function at; https://brainly.com/question/2284808
Jason is buying a home theater system on layaway for $349. If he makes a down payment of $25 and pays $54 each week will it take Jason to pay for the home theater system?
Jason will take 6 weeks to pay off the home theater system on layaway after making an initial down payment of $25 and weekly payments of $54.
The student's question is about how long it will take Jason to pay for a home theater system using a layaway plan. Jason has made an initial down payment of $25 and will make weekly payments of $54.
To calculate the time it will take to pay off the remaining balance, we subtract the down payment from the total cost: $349 - $25 = $324. Then, we divide the remaining balance by the weekly payment amount: $324 / $54 = 6. This means it will take Jason 6 weeks to pay off the home theater system on layaway.
A child designs a flag in the shape of a rhombus, as shown in the diagram below. Which expression can be used to determine the side length of the rhombus?
Answer:
A
Step-by-step explanation:
10/cos30 degree
The distance between 2 points is found by ________ the x terms and squaring the result, _________ the y terms and squaring the result, taking the sum of the results and then finding the square root of the sum.
subtracting; subtracting
adding; adding
adding; subtracting
subtracting; adding
Answer:
A)
subtracting; subtracting
Step-by-step explanation:
Every morning, a deli offers a “commuter special” in which customers can select a pastry, beverage, and a copy of one of the local papers and pay $1.00. Their options are listed in the table.
Last Tuesday, the deli did not have any muffins. How did that affect the number of possible combinations?
A. It decreased the number of combinations by 1.
B. It decreased the number of combinations by 4.
C. It decreased the number of combinations by 8.
D. It decreased the number of combinations by 10.
Answer: C
c. It decreased the number of combinations by 8.
Turning of the water while brushing your teeth saves 379 centiliters off water . how many liters of water can you save if you turn of the water while you brush three times'
It's been estimated that if you consume an extra 3,500 calories, you will gain 1 pound of fat. one can of soda contains 40 grams of sugar. sugar has 4 calories per gram. if a person drinks a six-pack of soda every day, how many pounds will he or she gain in 1 year?
Heather is writing a quadratic function that represents a parabola that touches but does not cross the x-axis at x = –6. Which function could Heather be writing?
Heather's quadratic function must have a double root at x = -6, suggesting a function of the form y = a(x + 6)² here 'a' is a nonzero coefficient. The orientation and width of the parabola depend on the value of 'a'.
Since Heather's quadratic function represents a parabola that touches but does not cross the x-axis at x =
–6, her function must have a double root at x= –6. To achieve this, the quadratic function should be in the form y = a(x + 6), where a is a non-zero coefficient.
The function that Heather could be writing will have a vertex at the point (-6, 0), as the parabola touches the x-axis at this point. Thus, a possible function can be y = (x + 6), if we assume a coefficient of 1 for simplicity. If a is negative, the parabola will open downwards, while a positive a will make the parabola open upwards. However, the exact value of a will depend on other conditions Heather might have, such as the position of the parabola in relation to the y-axis or specific points it must pass through.
Please help me !! Thank you!!
What is the solution to 2h+8>3h-6
He perimeter of this pentagon is 280 cm. find the lengths of the sides.
please help thank you
.hey can you help me I will crown you brainliest
Charlie is trying to hold on to his toy fire truck.
His brother Noah is pulling with a force of 8 N on a bearing of 023° and his brother Jude with a force of 5 N on a bearing of 155°.
What force does Charlie need to exert to keep the toy in equilibrium?
If you could explain it using Cartesian vectors, that would be the best.
Charlie needs to apply a force in the opposite direction of the resultant vector sum of his brothers' forces. By converting the forces into Cartesian vectors based on the bearings, we can calculate the components of Charlie's required force to maintain equilibrium.
Explanation:Step 1: Break down the forces into their x and y components
The force exerted by Noah can be broken down into its x and y components using the following equations:
F_x_Noah = F_Noah × cos(θ_Noah) = 8 N × cos(023°) ≈ 7.13 N
F_y_Noah = F_Noah × sin(θ_Noah) = 8 N × sin(023°) ≈ 3.71 N
The force exerted by Jude can be broken down into its x and y components using the following equations:
F_x_Jude = F_Jude × cos(θ_Jude) = 5 N × cos(155°) ≈ -4.95 N
F_y_Jude = F_Jude × sin(θ_Jude) = 5 N × sin(155°) ≈ -0.58 N
Step 2: Sum the x and y components of the forces
To find the net force in the x-direction, we sum the x-components of the forces exerted by Noah and Jude:
F_x_net = F_x_Noah + F_x_Jude ≈ 7.13 N - 4.95 N ≈ 2.18 N
To find the net force in the y-direction, we sum the y-components of the forces exerted by Noah and Jude:
F_y_net = F_y_Noah + F_y_Jude ≈ 3.71 N - 0.58 N ≈ 3.13 N
Step 3: Calculate the magnitude of the net force
The magnitude of the net force can be calculated using the Pythagorean theorem:
F_net = √(F_x_net^2 + F_y_net^2) ≈ √(2.18 N^2 + 3.13 N^2) ≈ 3.74 N
Step 4: Find the angle of the net force
The angle of the net force can be calculated using the following equation:
θ_net = atan(F_y_net / F_x_net) ≈ atan(3.13 N / 2.18 N) ≈ 55.6°
Step 5: Calculate the force Charlie needs to exert
In order for Charlie to keep the toy fire truck in equilibrium, he needs to exert a force that is equal in magnitude and opposite in direction to the net force. Therefore, the force Charlie needs to exert is 3.74 N at an angle of 55.6° + 180° = 235.6° (since the net force is acting in the third quadrant).
A bank's monthly charge for maintaining an account is $.45 for each check written plus a service charge of $12.50. If x represents the number of checks written during the month, which function models this situation?
A) f(x) = x + 12.50
B) f(x) = 0.45x -12.50
C) f(x) = 12.50x + 0.45
D) f(x) = 0.45x + 12.50
The correct model for the bank service cost based on the number of checks written during a month is f(x)=0.45x + 12.50.
Explanation:The question is asking for a model that would represent the cost of a bank service based on the number of checks written during a month. The bank charges $0.45 for each check, which is a variable cost that will change depending on the number of checks, represented by x. Additionally, they also have a monthly fixed service charge of $12.50, which is paid regardless of whether or not a check is written that month.
So, the amount paid every month is $0.45 multiplied by the number of checks, plus $12.50. In function format, that will be represented as $0.45x + $12.50, which is equivalent to the option D i.e f(x)=0.45x + 12.50. So, the correct model for the situation is D.
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A rectangle has a length of 12 millimeters and a width of 17 millimeters.
What is the effect on the perimeter when the dimensions are multiplied by 12?
a. The perimeter is increased by a factor of 12.
b. The perimeter is increased by a factor of 48.
c. The perimeter is increased by a factor of 144.
d. The perimeter is increased by a factor of 576.
ok so original perimeter = 12 +12 + 17 +17 = 58 mm
if dimensions are multiplied by 12:
12*12 = 144 and 17*12 = 204
new perimeter = 144 +144 +204 +204 = 696 mm
696 / 58 = 12
so the perimeter increased by a factor of 12, answer is A
Answer:
The perimeter is increased by a factor of 12.
Option (a) is correct .
Step-by-step explanation:
Formula
Perimeter of a rectangle = 2 (Length + Breadth)
As given
A rectangle has a length of 12 millimeters and a width of 17 millimeters.
Perimeter of a rectangle = 2 × (12 + 17)
= 2 × 29
= 58 millimeters ²
As given
when the dimensions are multiplied by 12 .
New Length = 12 × 12
= 144 millimeter
New Breadth = 17 × 12
= 204 millimeter
Thus
New Perimeter of a rectangle = 2 × (144 + 204)
= 2 × 348
= 696 millimeter²
[tex]\frac{New\ perimeter\ of\ a\ rectangle}{Perimeter\ of\ a\ rectangle} = \frac{696}{58}[/tex]
[tex]\frac{New\ perimeter\ of\ a\ rectangle}{Perimeter\ of\ a\ rectangle} = 12[/tex]
Therefore the perimeter is increased by a factor of 12.
Option (a) is correct .
The area of the blue triangle, which is one-half times a base of 47 million times a height of $37.89.
Using the formula v= l x w x h find the volume of a right rectangular prism when the length of the prism is 45cm the width is 12cm and height is 10cm
The volume of the right rectangular prism is 5400 cubic centimeter.
What is right rectangular prism?
A right rectangular prism is a three dimensional object with six faces, twelve edges, and eight vertices.
Formula for the volume of right rectangular prism:volume of right rectangular prism = length × width × height
According to the given question we have,
length of the prism = 45cm
width of the prism = 12cm
height of the prism = 10cm
Therefore,
The volume of the right rectangular prism = length × width × height
⇒ volume of prism = 45 × 12 × 10 = 5400 cubic centimeter.
Hence, the volume of the right rectangular prism is 5400 cubic centimeter.
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Tell whether each sequence is arithmetic. Justify your answer. If the sequence is arithmetic, write a function rule to represent it. A. 128, 64, 32, 16, ... B. 3, 3.25, 3.5, 3.75, ...
What is the solution to the system of equations below? Y=-4/5x-6 & y=-30
The solution of the system is y = -30 and x = 30.
How to solve the system of equations?Here we have two equations:
y = -(4/5)*x - 6
y = -30
The second equation can be replaced in the first one, so we get:
-30 = -(4/5)*x - 6
Now we can solve that for x.
-30 + 6 = -(4/5)*x
24*(5/4) = x = 30
So the solution of the system is y = -30 and x = 30.
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Which unit should be studied to review symbols from set theory? Unit 1 Unit 3 Unit 5 Unit 7
While training for a marathon, Sean runs at least 28 miles a week. He has already ran 6 miles this week. The inequality shown can be used to find m, the number of miles Sean still needs to run this week. m + 6 ≥ 28 Which inequality represents the solution set for this situation? A) m ≥ 22 B) m ≤ 22 C) m ≤ 34 D) m ≥ 34
Answer: A) m ≥ 22
Step-by-step explanation:
Hi, to answer this question we simply have to solve the inequality given for m (miles ran per week).
m + 6 ≥ 28
Subtracting 6 from both sides:
m+6-6 ≥ 28 -6
m ≥ 22
Sean still needs to run 22 miles this week.
So, the correct option is A) m ≥ 22
Feel free to ask for more if needed or if you did not understand something.
You work as a coordinator for data entry projects. On one project, the status report shows that 15% of the work was completed in 6 days. If the work progresses at the same rate, how many more days will be required to complete the remainder of the project?
Answer: They need 34 more days to complete the remainder of the project.
Step-by-step explanation:
Since we have given that
Number of days the work was done = 6 days
Part of work is completed in these days = 15%
If the work is done at the same rate,
then the remaining part of work is done in how many days.
Remaining part of work is 100% - 15% = 85 %
So, it becomes,
[tex]\dfrac{6}{0.15}=\dfrac{x}{0.85}\\\\x=\dfrac{6\times 0.85}{0.15}=34\ days[/tex]
Hence, they need 34 more days to complete the remainder of the project.
One reading list had a total of 12 fiction and nonfiction books. Compared to the first list, there are twice as many fiction books and 3 times as many nonfiction books making a total of 28 books on the second reading list. Write a system of linear equations and find the number of fiction and nonfiction books on the first list.
Answer:
(8,4)
Step-by-step explanation:
yes
Write a polynomial function of f of least degree with rational coefficients a leading coefficient of 1 and the given zeros -5 2i
a wheel has a radius of 12 cm approximately how far does it travel in 2 revolutions
Hello!
S=R*THETA
so s= is what you are looking for.
givens;
radius=12cm=.12m
theta(RADIANS ONLY)=2pi*2revs=4pi
s=.12*4pi=for an approximate answer of 1.50796m travelled
hope this helps. any questions please ask. thank you
Dan and Dawn purchased a house for $69,500. They had to make a down
payment of 20%. How much was the amount of the mortgage they obtained?
a. $13,900
b. $69,500
c. $55,600
d. $76,450
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The simplest form of square root of eighty can be written as a times square root of b, where a = and b = .
The correct answer is:
A=4
B=5
hopes this helps you and future people!
Answer:
a = 4 and b = 5
Step-by-step explanation:
The simplest form of square root of eighty can be written as:
[tex]\sqrt{80}=\sqrt{2\times2\times2\times2\times5}[/tex]
Now as it is a square root function, we will pair up the four 2's in two pairs.
And will take out [tex]2\times2[/tex] outside the square root.
Making the answer = [tex]2\times2\sqrt{5}[/tex]
or [tex]4\sqrt{5}[/tex]
So, a = 4
and b = 5
find the nonpermissible replacement for y in this expression Y+7/Y-3
Final answer:
The nonpermissible value for y in the expression (Y+7)/(Y-3) is 3, because it would make the denominator zero, resulting in an undefined expression.
Explanation:
The question is asking to find the nonpermissible value for y in the expression (Y+7)/(Y-3). In algebra, nonpermissible values are values for the variable that would make the denominator of a fraction equal to zero. We set the denominator of our expression equal to zero and solve for y.
Steps to find the nonpermissible value:
Identify the denominator of the expression, which is (Y-3).
Set the denominator equal to zero: Y - 3 = 0.
Solve for y: Y = 3.
Therefore, the nonpermissible replacement for y is 3, as substituting this value into the denominator would create a division by zero, which is undefined in mathematics.
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Choose the option that correctly completes the statement.
The measure of an exterior angle of a triangle is _____ the sum of the measures of the remote interior angles.
less than
greater than
equal to
The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
Explanation:The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
For any triangle, the sum of the measures of the three interior angles is always 180 degrees. An exterior angle is formed by extending one side of the triangle. The sum of the measures of the exterior angle and its corresponding remote interior angles is always 180 degrees. Therefore, the measure of an exterior angle is equal to the sum of the measures of the remote interior angles.
Final answer:
The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
Explanation:
The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.
For example, if one of the remote interior angles of a triangle measures 40 degrees, then the corresponding exterior angle measures 40 degrees as well. The sum of the measures of the other two interior angles would be 140 degrees, making the exterior angle equal to 40 degrees.
Therefore, the correct option that completes the statement is equal to.