Answer:
[tex](f-g)(4) = -59[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]f(x)=4x-3\text{ and } g(x) = x^3 +2x[/tex]
And we want to find the value of:
[tex](f-g)(4)[/tex]
Recall that this is equivalent to:
[tex](f-g)(4) = f(4) - g(4)[/tex]
Find f(4):
[tex]f(4) = 4(4)-3 = 13[/tex]
And find g(4):
[tex]g(4) = (4)^3 + 2(4) =72[/tex]
Substitute:
[tex](f-g)(4) = (13)-(72)[/tex]
And subtract. Hence:
[tex](f-g)(4) = -59[/tex]
Step-by-step explanation:
I love this question!
So there are a couple different ways of solving this. You feel free to ignore whichever one makes less sense.
Subtracting First
The first option is taking f(x) and g(x) and subtracting them, then introducing the number.
The calculation:
f(x) - g(x)
Substitute.
4x - 3 - (x^3 + 2x)
Multiply out the negative.
4x - 3 - x^3 - 2x
Rewrite.
-x^3 + 4x - 2x - 3
Simplify.
-x^3 + 2x - 3
Then, replace x with 4.
-(4)^3 + 2(4) - 3
Simplify.
-64 + 8 - 3
Add.
-59
Making x = 4 first
Here, we'll do what's on the tin. Find f(4) and g(4), then subtract them.
f(x) = 4x - 3
f(4) = 4(4) - 3
f(4) = 16 - 3
f(4) = 13
Then find g(4):
g(x) = x^3 + 2x
g(4) = (4)^3 + 2(4)
g(4) = 64 + 8
g(4) = 72
Then, subtract these two:
f(4) - g(4) = 13 - 72
f(4) - g(4) = -59
Answer:
Either way, the answer is -59
help please! I need the answer quickly! thank you!
Answer:
B) 1 unit to the left
Step-by-step explanation:
Write the solution for x+5≤8 x + 5 ≤ 8 in set notation
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Answer:
{x ∈ ℝ | x ≤ 3}
Step-by-step explanation:
Subtracting 5 from both sides, we see the solution is ...
x ≤ 3
In set notation, this can be written ...
{x ∈ ℝ | x ≤ 3}
properties of exponents. the answer is 1/2^3 i need help with the work
(2^-1)^2/2×2^0
2^(-1×2)/2^1
2^-2/2^1
2^(-2-1)
2^(-3)
(1/2)^3
Properties used (m^n)^a = m^na
(m)^-n = (1/m)^n
m^0 = 1
m^n/m^a = m^(n-a)
Must click thanks and mark brainliest
PLEASE HELPPPPPPPPPP
Answer:
167/346 or 0.483
Step-by-step explanation:
From the question given above, the following data were obtained:
Number of Tails (T) = 167
Number of Heads (H) = 179
Probability of tail, P(T) =?
Next, we shall determine total outcome. This can be obtained as follow:
Number of Tails (T) = 167
Number of Heads (H) = 179
Total outcome (S) =?
S = T + H
S = 167 + 179
Total outcome (S) = 346
Finally, we shall determine the probability of tails. This can be obtained as follow:
Number of Tails (T) = 167
Total outcome (S) = 346
Probability of tail, P(T) =?
P(T) = T / S
P(T) = 167 / 346
P(T) = 0.483
Thus, the probability of tails is 167/346 or 0.483
-12x + 12 = 4 - 15x + 9
Answer:
x = 1/3
Step-by-step explanation:
-12x + 12 = 4 - 15x + 9
Combine like terms
-12x +12 = -15x+13
Add 15x to each side
-12x+12 +15x = -15x+15x+13
3x+12 = 13
Subtract 12 from each side
3x+12-12 = 13-12
3x = 1
Divide by 3
3x/3 = 1/3
x = 1/3
Sydney has finished all his work on time, but many of his teammates are still struggling to complete their assignments. What should he do? a) Not distract them; they may get farther behind. O b) Listen to them complain about their workloads O c) Help them complete their work d) Share his thoughts on how they could get their work done faster
Answer:
I think the correct option is c
Answer:
I think the correct answer is (d)
Step-by-step explanation:
if he shares his thoughts on how they could get their work done faster like using an app like this, then it would be of great help to them
The product of the roots of the equation x2 + x=2 is:
0-2
01
Answer:
-2
Step-by-step explanation:
x^2 + x=2
Subtract 2 from each side
x^2 + x-2=2-2
x^2 + x-2=0
Factor
What 2 numbers multiply to -2 and add to 1
2*-1 = -2
2+-1 =1
(x-1)(x+2)=0
Using the zero product property
x-1 = 0 x+2 = 0
x=1 x = -2
Product of the roots
1*-2 = -2
identify an equation in point slope form for the line perpendicular to the y=-1/2x+11 that passes through (4,-8). a. y+8=1/2(x-4) b. y-4=2(x+8) c. y-8=1/2(x+4) d. y+8=2(x-4)
Answer:
d. y+8=2(x-4)
Step-by-step explanation:
There are 2 important parts to this question. First, understanding which slopes are perpendicular. The negative reciprocal of a number will be perpendicular to it. So, since the original slope is -1/2 the new slope should be 2.
Then, remember what the point-slope formula is. The point-slope formula is: [tex]y-y_{2}=m(x-x_{2})[/tex]. So if you plug in the point and slope the new equation looks like, [tex]y--8=2(x-4)[/tex]. Then, simplify for the final answer of [tex]y+8=2(x-4)[/tex].
A toddler is allowed to dress himself on Mondays, Wednesdays, and Fridays. For each of his shirt, pants, and shoes, he is equally likely to put it on correctly as incorrectly. Getting these articles of clothing on correctly are independent of each other. On the other days, the mother dresses the toddler with 100% accuracy. Given that the toddler is correctly dressed, what is the probability that today is Monday
Answer:
0.0286 = 2.86% probability that today is Monday.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Dressed correctly
Event B: Monday
Probability of being dressed correctly:
100% = 1 out of 4/7(mom dresses).
(0.5)^3 = 0.125 out of 3/7(toddler dresses himself). So
[tex]P(A) = 0.125\frac{3}{7} + \frac{4}{7} = \frac{0.125*3 + 4}{7} = \frac{4.375}{7} = 0.625[/tex]
Probability of being dressed correctly and being Monday:
The toddler dresses himself on Monday, so (0.5)^3 = 0.125 probability of him being dressed correctly, 1/7 probability of being Monday, so:
[tex]P(A \cap B) = 0.125\frac{1}{7} = 0.0179[/tex]
What is the probability that today is Monday?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0179}{0.625} = 0.0286[/tex]
0.0286 = 2.86% probability that today is Monday.
I need you guy’s help answer thanks so much
Answer:
D
Step-by-step explanation:
inverse just means opposite so if its shown dividing it first then adding, then the inverse is multiplying then subtracting
Given the following coordinates complete the glide reflection transformation.
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Answer:
A"(-1, -2)B"(4, 0)C"(6, -3)Step-by-step explanation:
The reflection over the x-axis is ...
(x, y) ⇒ (x, -y)
The shift left 3 units is ...
(x, y) ⇒ (x -3, y)
So, the two transformations together will be ...
(x, y) ⇒ (x -3, -y)
A(4, 2) ⇒ A"(1, -2)
B(7,0) ⇒ B"(4, 0)
C(9, 3) ⇒ C"(6, -3)
Need help ASAP no links pls
Answer:
y = 6
I hope this helps you out!
james invested some money at 13% interest. James also invested $199 more than 3 times that amount at 12%. How much is invested at each rate if James receives $1561.50 in interest after one year? (Round to two decimal places if necessary.)
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Answer:
$3138 at 13%9613 at 12%Step-by-step explanation:
Let x represent the amount invested at 13%. Then (3x+199) is the amount invested at 12%. The total interest earned in 1 year is ...
(13%)(x) +(12%)(3x+199) = 1561.50
0.49x +23.88 = 1561.50 . . . . simplify
0.49x = 1537.62 . . . . . . . . . . subtract 23.88
x = 3138 . . . . . . . . . . . . . . . . divide by 0.49
3x+199 = 9613
$3138 was invested at 13%; $9613 was invested at 12%.
Can somebody help me find the answer to this problem please ?
Answer:
Step-by-step explanation:
Answer:
D. x = -2y + 4
Step-by-step explanation:
4x + 8y = 16
Solve for x
Our objective here is to isolate x ( in other words we want to get x by itself ) using inverse operations.
So let's begin
4x + 8y = 16
First we want to get rid of 8y
Notice how 8y is being added to 4x
Well we can get rid of it by applying it's inverse operation. The opposite of addition is subtraction. So to get rid of 8y we would simply subtract 8y.
Important note! Whatever we do to one side we must do to the other
So we would subtract 8y from both sides
4x + 8y - 8y = 16 - 8y
The 8y on the left hand side cancels out and the 8y on the right side stays as it is as you can't subtract 8y from 16
We then have 4x = 16 - 8y
Next we want to get rid of 4 from 4x.
4x is the same as 4*x which is multiplication
The inverse of multiplication is division so to get rid of the 4 we divide both sides by 4
4x/4 = (16-8y)/4
4x/4 = x
16-8y/4 ( simply divide 16 by 4 and -8y by 4 )
16-8y/4 = 4 - 2y
We're left with x = 4 - 2y which can also be written as x = -2y + 4
If a over 2 equals b over 3 then b over a equals what?
What is the perimeter of the octagon below!!
Answer:
C) sixty five units
Step-by-step explanation:
have a great day
❤❤❤PLEASE BE RIGHT AND CORRECT BEFORE ANSWERING
Answer:
y=-x+28
Step-by-step explanation:
The slope(rise/run) is -1, and because it starts at y=28, the answer is y=-x+28
Answer:
"C"
The slope is -2 !!! delta y = 20 delta x = 10
the y intercept is 28
Step-by-step explanation:
QUESTION 9
Each person drinks half a litre carton of orange juice. How many cartons of orange juice do Joe's guests drink in total?
Consider the triangle ΔXYZ . Find the angle Z given that ZY=30 , ZX=15 , and YX=21
Step-by-step explanation:
hey bro can get the diagram
Answer:
where is the diagram plz show the diagram
Step-by-step explanation:
The three sides of a triangle are n, 3n+3, and 3n−1. If the perimeter of the triangle is 72m, what is the length of each side?
Answer: 10m, 33m, and 29m
Step-by-step explanation:
n + 3n+3 + 3n-1 = 72m
7n+2=72m
7n = 72-2
n = 70/7
n = 10
Write two ratios equivalent to 24 : 9.
Answer:
8:3
16:6
Step-by-step explanation:
First, let's check if 9 and 24 have any common factor. If they do have any common ones, we must find the GCF (greatest common factor).
Factors of 9: 1, 3, 9
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The common factors both of the numbers share and 1 and 3. To find the GCF, simply compare one of the factors to the other.
1 < 3
Now that we know the GCF, we can divide the two numbers in the ratio 24 : 9 by it (3).
24:9
24/3:9/3
8:3
Now that our ratio is simplified, it's going to be much easier to find more ratios that are equivalent. 8:3 is already one equivalent ratio, but if we multiply each number in the ratio by any other number, we can get a new equivalent ratio. Let's multiply each number in the ratio by 2:
8:3
8 ⋅ 2:3 ⋅ 2
16:6
So, another equivalent ratio to 24:9 (and 8:3) is 16:6.
I need to know this answe ASAP
Answer:
look at the value of f(x) carefully when we put 7 from x the x take 2 value
Step-by-step explanation:
And g(x) function take 4 value. please look at the first option it has extra 2 so 2 plus 2 equal to 4 this means that the answer might be A. But look at D option it multiply by 2 so D option might be correct answer but we need some info and I want to continue. When I put 1 from x f(x)=1 and g(x)= 2 but when we look at the first option it is 1+2 equal to 3 but it must be 2 so the correct answer is not A and the correct answer is D
A group of friends try out a new game that uses a pair of ordinary, fair dice. Points are given to players based on the sum of the two numbers from the rolled pair of dice. If the sum is between 2 and 5, inclusive, the amount of points awarded is the sum minus 1. If the sum is between 6 and 9, inclusive, the amount of points awarded is the sum minus 3. If the sum is between 10 and 12, inclusive, the amount of points awarded is the sum minus 5. Calculate the probability of earning exactly 5 points.
Answer:
0.2222 = 22.22% probability of earning exactly 5 points.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Possible outcomes:
For the pair of dice:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
So 36 total outcomes.
If the sum is between 6 and 9, inclusive, the amount of points awarded is the sum minus 3.
Sum of 8 -> 5 points awarded. So
(2,6), (3,5), (4,4), (5,3), (6,2): 5 outcomes.
If the sum is between 10 and 12, inclusive, the amount of points awarded is the sum minus 5.
Sum of 10 -> 5 points awarded. So
(4,6), (5,5), (6,4): 3 outcomes.
Desired outcomes:
5 + 3 = 8
Calculate the probability of earning exactly 5 points.
[tex]p = \frac{D}{T} = \frac{8}{36} = 0.2222[/tex]
0.2222 = 22.22% probability of earning exactly 5 points.
Need help pls will give brainly
2) Consider the quadratic sequence 72, 100, 120, 132
2.1.1) Determine Tn the nth term of the quadratic.
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Answer:
Tn = -4n² +40n +36
Step-by-step explanation:
A graphing calculator readily performs the quadratic regression, yielding the formula ...
Tn = -4n² +40n +36
__
The first and second differences of the given sequence terms are ...
28, 20, 12 and -8, -8
The coefficient of the squared term is half the second difference, so is -4. Then the sequence of squared terms is -4n²:
-4, -16, -36, -64
Subtracting these values from the original sequence gives the linear sequence ...
76, 116, 156, 196
which has first term 76 and common difference 40. The equation for the n-th term of this is ...
an = 76 +40(n -1) = 36 +40n
Adding this linear sequence to the sequence of squared terms, we get ...
Tn = -4n² +40n +36
Two lines, A and B, are represented by equations given below:
Line A: y = x − 2
Line B: y = 3x + 4
Which of the following shows the solution to the system of equations and explains why?
(−3, −5), because the point does not lie on any axis
(−3, −5), because the point satisfies both equations
(−4, −8), because the point satisfies one of the equations
(−4, −8), because the point lies between the two axes
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Answer:
(b) (−3, −5), because the point satisfies both equations
Step-by-step explanation:
Any solution to a system of two equations must satisfy both equations. The only reasonable explanation of "why" is the one associated with the answer shown above.
PLEASE ANSWER QUICK ITS BEEN 1 HOUR
Which of the following is a unit rate?
A. 4 Feet / 1 Second
B. 120 Miles / 2 Hours
C. $1.25 / 4 oz
D. 340 Miles / 6 Gallons
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Answer:
A. 4 feet/(1 second)
Step-by-step explanation:
A "unit" is one of something. A unit rate is a rate that has 1 of something in the denominator. Look down the list at the denominators and find the value that has 1 as a denominator:
[tex]\dfrac{4\text{ feet}}{1\text{ second}}[/tex]
Please due in 1 hour
I hope that helped you
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Answer:
d + q = 440.10d +0.25q = 8.30Step-by-step explanation:
The first equation describes the total number of coins. It says the sum of the numbers of dimes and quarters is 44, the total number of coins.
__
The second equation describes the total value of the coins. It will say that 0.10 times the number of dimes plus 0.25 times the number of quarters is 8.30, the total dollar value of the coins.
The two equations are ...
d + q = 44
0.10d +0.25q = 8.30
__
Additional comment
The solution can be found by substituting for d:
0.10(44 -q) +0.25q = 8.30
0.15q = 3.90
q = 26
d = 44 -26 = 18
Vinnie has 18 dimes and 26 quarters in his bag.
6. How many four digit numbers can be formed, using
7,5, 0, 2 only once in a number?
(A). 4
(B). 12
(C).9
(D). 18
Answer:
Letter D
Step-by-step explanation:
18 is your answer
Please Help!
Function: y=x^2+5x-7
Vertex: (___,___)
Solutions: (___,___) and (___,___)
* i thought the vertex was (-5/2,-53,4) but apparently i’m wrong since it keeps saying it* i need answers please
Answer:
Step-by-step explanation:
