Answer:
[tex]\frac{dy}{dx} = 24 x + 21[/tex]
Step-by-step explanation:
Explanation:-
Given that the function
y = f(x) = 3 x ( 4 x + 7)
y = 3 x ( 4 x + 7)
y = 12 x² + 21 x ..(i)
Differentiating equation (i) with respective to 'x' , we get
[tex]\frac{dy}{dx} = 12 (2x) +21 (1)[/tex]
[tex]\frac{dy}{dx} = 24 x + 21[/tex]
what is the P.O.I for 5.2x-y=4 1/2x+y=1
Answer:
X = 4/13
Y = - 5/13
Step-by-step explanation:
Since all of the equalities are true, the ordered pair is the solution of the system
The following sample data are from a normal population: 10, 8, 12, 15, 13, 11, 6, 5. (a) What is the point estimate of the population mean? 8.75 Incorrect: Your answer is incorrect. (b) What is the point estimate of the population standard deviation? (Round your answer to three decimal places.) (c) With 95% confidence, what is the margin of error for the estimation of the population mean? (Round your answer to one decimal place.) (d) What is the 95% confidence interval for the population mean? (Round your answer to one decimal place.) to
Answer:
10 ; 3.464 ; 2.4 ; (7.6, 12.4)
Step-by-step explanation:
Given the data :
10, 8, 12, 15, 13, 11, 6, 5
Point estimate of population mean :
m = ΣX / n
n = sample size = 8
(10+8+12+15+13+11+6+5) / 8
= 10
Point estimate of population standard deviation :
Sqrt(Σ(X - m)^2 / n-1)
((10-10)^2 + (8-10)^2 + (12-10)^2 + (15-10)^2 + (13 - 10)^2 + (11-10)^2 + (6-10)^2 + (5-10)^2) / 7
= sqrt(84/7)
= 3.464
Margin of error at 95%:
Zcritical * sqrt(sd²/n)
Zcritical at 95% = 1.96
1.96 * sqrt(3.464^2 / 8)
Margin of Error = 2.4
Confidence interval :
m ± Z(s/sqrt(n))
10 - 1.96(3.4634/sqrt(8)) = 7.6
10 - 1.96(3.4634/sqrt(8)) = 12.4
Katherine D’Ann is planning to finance her college education by selling programs at the football games for State University. There is a fixed cost of $400 for printing these programs, and the variable cost is $3. There is also a $1,000 fee that is paid to the university for the right to sell these programs. If Katherine was able to sell programs for $5 each, how many would she have to sell in order to break even?
Answer:
700 programs
Step-by-step explanation:
Given that :
Fixed cost = $400
Variable cost = $3 per program
Right to sell fee = $1000
Sales price per program = $5
Let number of programs sold = x
In other to break even, expense = revenue
(Fixed cost + variable cost per program + right to sell fee) = sales price per program
(400 + 3x + 1000) = 5x
1400 + 3x = 5x
1400 = 5x - 3x
1400 = 2x
1400 / 2 = x
x = 700
Number of programs to be sold in other to break even = 700
Here are the first four terms of a number sequence.
8
14
20
26
Write down the next term of the number sequence and explain how you found your answer
Megan and noah were splitting nachos. Megan ate 1/4 of the nachos and noah ate 5/12 of the nachps. What fraction of the nachos did they eat
Answer:
3/5
Step-by-step explanation:
Answer:
They ate 6/12 of the nacho
Step-by-step explanation:
hope that helps
Find the size of the angle a.
Diagram not drawn accurately
Answer:
45°
Step-by-step explanation:
Since,
3a + a + 2a + 2a = 360°
What’s the answer please??
Answer:
your answer will be x=1.13504161
9514 1404 393
Answer:
{-1.47, 1.14}
Step-by-step explanation:
The solution to ...
ax^2 +bx +c = 0 is ...
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
Filling in the values a=3, b=1, c=-5, the solutions are ...
[tex]x=\dfrac{-1\pm\sqrt{1^2-4(3)(-5)}}{2(3)}=\dfrac{-1\pm\sqrt{61}}{6}\\\\\boxed{x\approx\{-1.47,1.14\}}[/tex]
what is the area of this quadrilateral?
Answer
theres nothing there
Step-by-step explanation:
You prob forgot to provide one
What is the square root of nine
Answer: the square root of 9 is 3.
Fill in the missing
number to make the
number sentence
true.
| 148 +___= 179
Answer: 31
Step-by-step explanation:
179 - 148 = 31
The answer is 31.
Step-by-step explanation:
179 -- 148 = 31.
148 + 31 = 179
A particle moves along the x-axis so that at time t≥0t\ge 0t≥0 its position is given by x(t)=−t3+6t2−9t+42.x(t)=-t^3+6t^2-9t+42.x(t)=−t3+6t2−9t+42. Determine the total distance traveled by the particle from 0≤t≤4.0\le t \le 4.0≤t≤4.
Answer: 4 units
Step-by-step explanation:
The given position function: [tex]x(t)=-t^3+6t^2-9t+42.[/tex], where t≥0.
To determine: Total distance traveled by the particle from 0≤ t ≤ 4.0.
At t=0,
[tex]x(0)=-(0)^3+6(0)^2-9(0)+42=42\\[/tex]
At, t=4,
[tex]x(4)=-(4)^3+6(4)^2-9(4)+42\\\\=-64+6(16)-36+42=38[/tex]
Total distance traveled by the particle from 0≤ t ≤ 4.0 = |42-38| units
= 4 units
Hence, the distance traveled by the particle from 0≤t≤4.0 is 4 units.
What is the solution to Three-fourths a greater-than negative 16?
a greater-than negative 21 and one-third
a less-than negative 21 and one-third
a greater-than 21 and one-third
a less-than 21 and one-third
will give brainliest
Answer:
a greater-than negative 21 and one-third
Step-by-step explanation:
3/4a>-16
divide both sides by 3/4
a>-16*4/3
a>-64/3
a>-21 1/3
so then
a greater-than negative 21 and one-third
Good luck on the test.
What is the value of the expression below when w=2 8w2+2w+8
Answer:
44?? maybe
Step-by-step explanation:
On an airplane flight, Steve watch the display that showed the number of minutes since the flight to cough and the number of miles away from the destination. He recorded various points and fit the line why equals 2426-8x To the data, Where x is The number of minutes flying and why is the number Have miles from the Have miles from the destination. According to the model, how far was Steve from his destination after 120 minutes of flying?destination A. 960 miles B. 2410 mikes C. 1466 !miles D. 3386 miles
Answer:
3386 miles was her destination......
Tyler was at the amusement park. He walked at a steady pace from the ticket booth to the bumper
cars.
The point on the graph shows his
arrival at the bumper cars. What do
the coordinates of the point tell us
about the situation?
What does the point (0,0) mean in
this situation?
What is the constant of
proportionality for the relationship
between time and distance? What
does it tell you about Tyler's walk?
Where do you see it in the graph?
9514 1404 393
Answer:
a) It took 40 seconds to go 50 meters from the ticket booth
b) Tyler started at the ticket booth
c) k = 5/4
d) Tyler walked at the rate of 1.25 meters per second
e) The constant of proportionality is the slope of the line from (0, 0) to (40, 50). It is not shown on the graph.
Step-by-step explanation:
a) The axis labels on the graph tell you that 40 represents the number of seconds of elapsed time, and 50 represents the number of meters from the ticket booth. With the information in the problem statement, the coordinates (40, 50) tell us it took Tyler 40 seconds to walk 50 meters from the ticket booth to the bumper cars.
__
b) The point (0, 0) tells us that Tyler started counting time when he left the ticket booth.
__
c) The constant of proportionality is the ratio of the second coordinate to the first. The constant of proportionality is 50/40 = 5/4 = 1.25. (Its units are meters per second.)
__
d) The constant of proportionality tells us that Tyler's steady pace was 1.25 meters per second.
__
e) The constant of proportionality is not shown on the graph. It is the slope of a line between the origin and the point (40, 50).
A car dealership uses the linear model y = -1100x + 25000 to
predict the depreciation of car values as time progresses. If x is how
old the vehicle is in years and y is the current value of the vehicle,
what will the value of the vehicle be 5 years after purchase?
a) $18,400
b) $19,500
d) $23,900
c) $22,700
Answer:
Graph the line using the slope and y-intercept, or two points.
Slope:
−
1000
-1000
y-intercept:
(
0
,
25000
)
(0,25000)
x
y
0
25000
25
0
xy025000250
Step-by-step explanation:
a
(づ￣ ³￣)づ
ALGEBRA II // MODULE 1
FUNCTIONS AND INVERSES - 1.2
1.2
READY, SET, GO!
Name
Period
Date
READY
Topic: Solving for a variable
Solve for x.
1.
17 = 5x + 2
2. 2x² – 5 = 3x2 – 12x +
31
3. 11 = 2x + 1
Answer:
1. x = 3
2.x = 6
3. x = 5
I hope this helps you :D
To solve for variables, we start by isolating the variable term and then solve for the variable. The values of x in the given equations are 3, 6 and 5, respectively.
Equation (1)
[tex]17 = 5x + 2[/tex]
Collect like terms
[tex]5x = 17 -2[/tex]
[tex]5x = 15[/tex]
Divide both sides by 5
[tex]x =3[/tex]
Equation (2)
[tex]2x^2 - 5 = 3x^2 - 12x + 31[/tex]
Collect like terms
[tex]3x^2 - 2x^2 - 12x + 31 +5=0[/tex]
[tex]x^2 - 12x + 36=0[/tex]
Expand
[tex]x^2 - 6x - 6x + 36=0[/tex]
Factorize
[tex]x(x - 6) - 6(x -6)=0[/tex]
Factor out x - 6
[tex](x - 6)(x -6)=0[/tex]
This means that:
[tex]x -6=0[/tex]
Solve for x
[tex]x = 6[/tex]
Equation (3):
[tex]11 = 2x + 1[/tex]
Collect like terms
[tex]2x = 11-1[/tex]
[tex]2x = 10[/tex]
Divide both sides by 2
[tex]x =5[/tex]
Hence, the values of x in the given equations are 3, 6 and 5.
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On a treasure map, a X is placed at point (9, -7). if the pirates are currently on point (9,3), how many units away are they?
Answer:
They are 10 units away from the treasure
Step-by-step explanation:
Notice that the points (9, -7) and (9, 3) are both located at the same x-value (9) while their y-values are in one case 3 units above the x-axis, and in the other 7 units BELOW the x-axis. Therefore thy differ by 3 - (-7) units , which totals 10 units.
How much longer is 3/8 foot than 1/8 foot?
Answer:
2/8 foot longer
Step-by-step explanation:
Help me I am suffering from math T-T
Answer:
7/10
Step-by-step explanation:
3 1/5= 16/5
2 1/2= 5/2
16/5=32/10
5/2=25/10
32/10 - 25/10 = 7/10
Answer:
7/10
Step-by-step explanation:
Step 1 : convert mixed fraction to improper fractions.
Step 2: Find Least common denominators.
Step 3 : Find equivalent fractions and subtract.
[tex]3\frac{1}{5}-2\frac{1}{2}= \frac{(3*5)+1}{5}-\frac{(2*2)+1}{2}\\[/tex]
[tex]= \frac{16}{5}-\frac{5}{2}\\\\=\frac{16*2}{5*2}-\frac{5*5}{2*5}\\\\=\frac{32}{10}-\frac{25}{10}\\\\= \frac{32-25}{10}\\\\= \frac{7}{10}[/tex]
Share 56 sweets in the ratio 2 : 5.
56 sweets can be shared in the ratio 2 : 5 as 16 sweets and 40 sweets.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, Share 56 sweets in the ratio 2 : 5.
First share is = (2/2+ 5)×56.
= (2/7)×56.
= 16.
And the second share is (5/2 + 5)×56.
= (5/7)×56.
= 40.
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How is a constant term different from a variable term
for an expression that represents a real-world situation?
Answer:
Constants are the terms in the algebraic expression that contain only numbers. That is, they're the termswithout variables. We call them constants because their value never changes, since there are no variablesin the term that can change its value.
Step-by-step explanation:
11. Which of the following points is on the
line 3x - 5y=1
A. (1, 2)
B. (2, 1)
C. (3/5, 1)
D. (2,3)
a
Step-by-step explanation:
because it's is very important
(GIVING BRAINLYIST) 3 pizzas are shared equally between 10 people. what fraction of a pizza does each person receive. show your work on a image or on paper with using fraction models! thank you for your help :D
Answer:
1/3
Step-by-step explanation:
Since there are ten people, you have to divide three by ten. It would be 1/3.
geometric mean of 384 and 6
Answer:
48 is the geometric mean of 384 and 6
The bakers at Healthy Bakery can make 310 bagels in 2 hours. How many
bagels can they bake in 20 hours? What was that rate per hour?
Answer:
The number of bagels made in 20 hours is 3100 bagels, at the rate of 155 bagels per hour.
Step-by-step explanation:
Given;
number of bagels in 2 hours = 310 bagels
The rate per hour is calculated as;
[tex]Rate = \frac{310 \ bagels}{2 \ hours}\\\\Rate = 155 \ bagels \ per \ hour[/tex]
In 20 hours, the number of bagels made is calculated as;
Number of bagels = 155 (bagels/hour) x 20 (hour)
= 3100 bagels.
Therefore, the number of bagels made in 20 hours is 3100 bagels, at the rate of 155 bagels per hour.
Plz help me with the problem
Answer:Step-by-step explanation:
Just tell me the problem
Find the Value of x in each figure.
[REFER TO ATTACHED PICTURE]
Answer:
First pic) x = 10
Second pic) x = 25
-
Step-by-step explanation:
☆9x - 15 is congruent to 7x + 5, meaning they equal the same. This is because they are vertical to each other
☆The equation would be a 9x - 15 = 7x + 5.
☆Let's solve it!
[tex] \: \: \: \: \: \: \: \: \: 9x - 15 = 7x + 5 \\ \frac{ - 7x \: \: \: \: \: \: \: = - 7x}{2x - 15 = 5} \\ \frac{ \: \: \: \: \: \: \: \: \: \: + 15 = + 15}{ \frac{2x}{2} = \frac{20}{2} } \\ \\ x = 10[/tex]
-------
☆2x + 15 and x are complementary angles, meaning they equal 90ndegrees together. This is because they lie on a right angle.
☆The equation would be: 2x + 15 + x = 90.
☆Let's solve it!
[tex]2x + 15 + x = 90 \\ 3x + 15 = 90 \\ \frac{ \: \: \: \: \: \: \: \: \: - 15 = - 15}{ \frac{3x}{3} = \frac{75}{3} } \\ \\ x = 25[/tex]
i only need 12 13 14
Use the information and diagram to answer the following question.
An airplane makes a 20° angle of elevation from the runway when it takes off.
The airplane shown is 2.500 feet along the ground from its take-off point.
Take-off point
20
2500 ft
Note: The figure is not drawn to scale.
At what height, h, is the airplane? Round the answer to the nearest foot. Show
your work.
Answer:
910 ft
Step-by-step explanation:
This question sets up the equation tan20°=x/2,500. Solve for X by multiplying 2,500 on both sides giving you x = 2,500tan20°. Finally, plug that in a calculator and you get 909.92. Round it to the nearest foot and you get 910
The required height where the plane is given as 910 ft, as of the given condition.
Given that,
An airplane makes a 20° angle of elevation from the runway when it takes off. The airplane shown is 2500 feet along the ground from its take-off point.
These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
here,
base length = 2500
Angle of inclination = 20°
let the perpendicular height = h
Now,
tan20° = h / base
h = 2500 [tan20°]
h = 910 ft
Thus, the required height where the plane is given as 910 ft, as of the given condition.
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