Answer:
(f - g)(x) = -x² + 4x + 4
General Formulas and Concepts:
Pre-Algebra
PropertiesAlgebra I
Combining like termsFunction notationStep-by-step explanation:
Step 1: Define
f(x) = 4x - 1
g(x) = x² - 5
(f - g)(x) = f(x) - g(x)
Step 2: Find
Substitute: (f - g)(x) = 4x - 1 - (x² - 5)Distribute: (f - g)(x) = 4x - 1 - x² + 5Combine like terms: (f - g)(x) = -x² + 4x + 4The product of two numbers is 1856. The sum is ninety. What is the difference of these two numbers?
======================================================
Explanation:
x and y are the two numbers
The product of those values is 1856, so xy = 1856
The sum is 90, so x+y = 90. Solve for y to get y = 90-x
Plug this into the first equation
xy = 1856
x(90-x) = 1856
90x-x^2 = 1856
0 = x^2-90x+1856
x^2-90x+1856 = 0
Now use the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-90)\pm\sqrt{(-90)^2-4(1)(1856)}}{2(1)}\\\\x = \frac{90\pm\sqrt{676}}{2}\\\\x = \frac{90\pm26}{2}\\\\x = \frac{90+26}{2} \ \text{ or } \ x = \frac{90-26}{2}\\\\x = \frac{116}{2} \ \text{ or } \ x = \frac{64}{2}\\\\x = 58 \ \text{ or } \ x = 32\\\\[/tex]
If x = 58, then,
y = 90-x
y = 90-58
y = 32
So one pair of values is (x,y) = (58,32)
We see that x*y = 58*32 = 1856
If x = 32, then,
y = 90-x
y = 90-32
y = 58
Showing (x,y) = (32,58) is the other solution. But this is just a mirror copy of the first solution. Effectively we're saying the same thing.
The two numbers 58 and 32 multiply to 1856, and they add to 90.
The difference in the two values is 58-32 = 26 which is the final answer.
------------------------
In summary,
58*32 = 1856
58+32 = 90
58 - 32 = 26
Answer:26
Step-by-step explanation:
x+y=90
xy=1856
x*(90-x)=1856
-x^2 +90x -1856=0
or x^2 -90x +1856=0
Using quadratic equation
(x-58)*(x-32)=0
x=58, y=32
58-32=26
A poll is given, showing 60% are in favor of a new building project. If 9 people are chosen at random, what is the probability that exactly 4 of them favor the new building project?
Answer:
The probability that exactly 4 are in favor the new building project is 0.1672.
Step-by-step explanation:
Let X denote the number of people who are in favor of a new building project.
The proportion of people who are in favor of a new building project is, p = 0.60.
A random sample of n = 9 people are chosen.
Every person has independent opinion about the new building project.
Thus, the random variable X follows a binomial distribution with parameters n = 9 and p = 0.60.
Compute the probability that exactly 4 are in favor the new building project as follows:
[tex]P(X=4)={9\choose 4}(0.60)^{4}(1-0.60)^{9-4}\\\\=126\times 0.1296\times 0.01024\\\\=0.167215104\\\\\approx 0.1672[/tex]
Thus, the probability that exactly 4 are in favor the new building project is 0.1672.
3(2e + 5) + 8(1 - e) = 1
ILL MARK BRAINLIST HELP !!!
Answer:
11 (positive)
Step-by-step explanation:
Answer:
e=11
Step-by-step explanation:
3(2e+5)+8(1-e)=1
6e+15+8-8e=1
-2e+23=1
-2e=-22
e=11
this one is also giving me a hard time
Answer:
Step-by-step explanation:
y = mx + b
[tex]m_{LN} = m_{NP }[/tex] = - [tex]\frac{10}{4}[/tex] = - [tex]\frac{5}{2}[/tex]
y-intercept is 1
y = - [tex]\frac{5}{2}[/tex] x + 1
Classwork
Example 1
Which of the following correctly models that the number of red gumballs is the number of white gumballs?
5
3
a.
Red
b.
Red
White
White
c.
Red
d.
Red
White
White
Answer:
b
Step-by-step explanation:
Each box represents 1/3. 5/3 of white is 2 boxes more so red needs 2 boxes more than white. 5 red and 3 white is the only one that follows the criteria.
hi guys whats 456829+345627=
you will win 85 points
Answer:
802456
Step-by-step explanation:
Brandon currently runs the mile in 6.8 minutes.
If he can cut 10 seconds off of his , -mile rate, what will his new mile time be?
I’m timed please help
The David family traveled to silver lake in five hours. Their return trip took 7/8 of the time it took to travel to the lake. How long did the return trip take
O 4 1/8
O 4 3/8
O 5 5/7
O 5 7/8
Please can someone help me
Answer:
60degree ...........
At Jay Street Middle School, 25%of eighth graders wear glasses. If 100 students wear glasses how many eighth graders are there in total?
Answer:
400 total
Step-by-step explanation:
so 100 is 25% of 100% and 25%x4=100%
so do 100x4=400=100% of the middle schoolers
6 + x = 6 help please
Answer:
The correct answer is that x = 0.
Answer:
x=0
Step-by-step explanation:
6+x=6
x=6-6
x=0
Please give the correct answer and I will give a brainless
Answer:
It’s 40 I’m pretty sure because of the square. That’s how I was taught.
The graph below shows the numbers of cups of peach juice that are mixed with different numbers of cups of lemon-lime soda to make servings of peach soda:
A graph is shown. The values on the x axis are 0, 1, 2, 3, 4, 5. The values on the y axis are 0, 9, 18, 27, 36, 45. Points are shown on ordered pairs 0, 0 and 1, 9 and 2, 18 and 3, 27 and 4, 36. These points are connected by a line. The label on the x axis is Lemon lime soda in cups. The title on the y axis is Peach juice in cups.
What is the ratio of the number of cups of peach juice to the number of cups of lemon-lime soda?
9:1
1:36
36:1
1:9
Answer:
A-9:1 is correct i can confirm since i took the test
Step-by-step explanation:
what are the possible values for the ones digits when a number is a multiple of 5
Answer:
0, 5
Step-by-step explanation:
5 * 0 = 0
5 * 1 = 5
5 * 2 = 10
5 * 3 = 15
5 * 4 = 20
5 * 5 = 25
etc.
Answer: 0, 5
If the ribbon costs 10 cents ($0.10) per foot, what is the total cost of the ribbon in dollars? Explain your reasoning.....how do you know where to place the decimal?
Answer:
The cost would be $0.10. You would figure this out because 10 cents is a 10th of a dollar
Step-by-step explanation:
Suppose 52R% of the population has a college degree. If a random sample of size 808808 is selected, what is the probability that the proportion of persons with a college degree will be less than 54T%
Answer:
The probability is [tex]P( p < 435.82 ) = 0.54094[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is p = 54% = 0.54
The sample size is n = 808
Generally the distribution of the population with college degree follows a binomial distribution
i.e
[tex]X \~ \ \ \ B(n , p)[/tex]
Generally the mean is mathematically represented as
[tex]\mu = n * p[/tex]
=> [tex]\mu = 808 * 0.52[/tex]
=> [tex]\mu = 420.16[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{np(1- p )}[/tex]
=> [tex]\sigma = \sqrt{808 * 0.52(1- 0.52 )}[/tex]
=> [tex]\sigma = 14.2[/tex]
Generally 54% of the population proportion is
[tex]\^ p = 0.54 * 808[/tex]
=> [tex]\^ p = 436.32[/tex]
Generally by normal approximation of the binomial distribution the probability that the proportion of persons with a college degree will be less than 54% is mathematically evaluated as
[tex]P(p < \^ p ) = P(\frac{p - \mu }{\sigma } < \frac{\^ p - \mu }{\sigma } )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
=> [tex]P(p < 436.32 ) = P( Z < \frac{436.32 - 420.16 }{14.20 } )[/tex]
applying continuity correction
[tex]P(p < (436.32-0.5) ) = P( Z < \frac{(436.32-0.5) - 420.16 }{14.20 } )[/tex]
=> [tex]P(p < (435.82 ) = P( Z < \frac{435.82 - 420.16 }{14.20 } )[/tex]
=> [tex]P(p < (435.82 ) = P( Z < 0.1028 )[/tex]
From the z table the area under the normal curve to the left corresponding to 0.1028 is
[tex]P( Z < 0.1028 ) = 0.54094[/tex]
=> [tex]P( p < 435.82 ) = 0.54094[/tex]
Which of the following relations between input numbers and output numbers is not a function?
Answer:
B
Step-by-step explanation:
If someone is smart enough to do this your a genius and I will give you a brainless
You have to fill in the blanks
I need help with this .
use the name of the graph to name the function
Find the smallest side of RST, given that
Answer:
doesn't it give you the angles for each letter? If that is the case then it would be 33
Step-by-step explanation:
May I have brainliest please? :)
Answer:
RT
Step-by-step explanation:
RT
Since angle S is the smallest angle, the smallest side is opposite that.
A boat is pulled toward a dock by means of a rope wound on a drum that is located 6 ft above the bow of the boat. If the rope is being pulled in at the rate of 5 ft/s, how fast (in ft/s) is the boat approaching the dock when it is 34 ft from the dock?
Answer:
Step-by-step explanation:
Given that:
The height of the dock (h) = 6
Let represent d to be the distance between the boat and the dock
Let the length of the rope between the boat and the drum be denoted by (l)
Then, the rate of change for the length of the rope be:
dl/dt = -5 ft/s
Using Pythagoras rule to determine the relationship between these values, we have:
[tex]l^2 = h^2 +d^2[/tex]
[tex]l^2 = 6^2 + d^2[/tex]
[tex]l^2 = 36 + d^2[/tex]
We relate to: [tex]2l * \dfrac{dl}{dt} = 2d* \dfrac{dd}{dt}[/tex]
From the question;
l = 34,
So to find [tex]\dfrac{dd}{dt}[/tex], we get;
[tex]d = \sqrt{l^2 - 36}[/tex]
[tex]d = \sqrt{34^2 - 36}[/tex]
[tex]d = \sqrt{1156- 36}[/tex]
[tex]d = \sqrt{1120}[/tex]
d = 33.46
So, we have:
[tex]\dfrac{dd}{dt}= \dfrac{l}{d} \times \dfrac{dl}{dt}[/tex]
[tex]\dfrac{dd}{dt}= \dfrac{34}{33.46} \times - 5[/tex]
[tex]\dfrac{dd}{dt}= 1.016 \times - 5[/tex]
[tex]\dfrac{dd}{dt}=-5.08 \ ft/sec[/tex]
Quick 50 points brainliest
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 11(1.01)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)
Answer:
[tex]0\leq d\leq 7[/tex]
Step-by-step explanation:
[tex]11.79=11(1.01^d)\\1.01^d=\frac{11.79}{11} \\1.01^d=1.0718\\ln(1.01^d)=ln(1.0718)\\d ln(1.01)=ln(1.0718)\\d=\frac{ln(1.0718)}{ln(1.01)} \\d=\frac{0.069}{0.0099} \\d=6.9696[/tex]
By rounding up.
d=7
Hence, the domain is
[tex]0\leq d\leq 7[/tex]
Answer:
0<x<d
its so easy if you need help
Help plzzzz I give extra points!
Answer: D
Step-by-step explanation:
3x-4 = -22
3x = -18
x= -6
Answer:
X = -6
Step-by-step explanation:
3x - 4 = -22
3x = -22 + 4
3x = -18
x = -18/3
x= -6
What volume would a 200 g sample of gold have, if its density is known to be 19.3
Answer:
The volume that a 200 g gold sample would have is 10.36 mL.
Step-by-step explanation:
Density is defined as the property that matter, whether solid, liquid or gas, has to compress into a given space. In other words, density is a quantity that allows us to measure the amount of mass in a certain volume of a substance. Then, the expression for the calculation of density is the quotient between the mass of a body and the volume it occupies:
[tex]density=\frac{mass}{volume}[/tex]
In this case it is known that the density of gold is 19.3 g / mL. This indicates that in 1 mL there are 19.3 g. Then the following rule of three can be applied: if 19.3 g is contained in 1 mL, how much volume is 200 g of gold?
[tex]volume=\frac{200 g*1mL}{19.3g}[/tex]
volume= 10.36 mL
The volume that a 200 g gold sample would have is 10.36 mL.
13/3 = 26/c help ASAP PLZ!!!!!!!!!!!!!
I suck at math I need help
Answer:
74° is the answer
In the triangle
112°+33°+a=180. (sum of angles of triangle)
a=180-145
a=35°
a+b+71°=180. (linear pair)
35°+b+71°=180
b=180-106
{b= 74°}
Josh is unpacking boxes at her job at target she unpacks 17 boxes that each have 25 regular DVDs in them she also on tax 24 boxes that each have a team blue rays TVs in them what is the total number of regular DVDs and Blu-ray’s that are on Pat Solve and explain
Answer:
1+1=4
Step-by-step explanation:
6. f(x) = (x + 2). g(X) = (X+3) Find (fºg)(x)
Answer:
(f o g)(x) = x + 5
General Formulas and Concepts:
Algebra I
Combining Like TermsAlgebra II
Function CompositionStep-by-step explanation:
Step 1: Define
f(x) = x + 2
g(x) = x + 3
(f o g)(x) = f(g(x))
Step 2: Find
Substitute: (f o g)(x) = (x + 3) + 2Combine like terms: (f o g)(x) = x + 5Answer:
f(x+3)=x+5
Goodluck to you
Solve the system
-3x+4y+2z=1
x+2y-z=6
2x-y+4z=7
Answer:
its A dont know how to explain it but i did the math and yes it is (2,3,1)
Step-by-step explanation:
Answer:
the answer is d (3,2,1) according to the picture given
Step-by-step explanation:
the system you wrote is different from the picture
Plz Help. Euler Equations are hard!
Find the general solution to the following differential equation.
An
2 pie/3
Step-by-step explanation: