The solution to (f + g) (x) is Option B: |2x +1| + 1
How to add functions?
We are given the functions;
f(x) = |2x +1| + 3
g(x) = -2
Now, we want to solve for (f + g) (x). From operations of functions, we know that there are different operations which could include addition, division, multiplication and subtraction. However, in this case;
(f + g) (x) simply means;
(f + g) (x) = f(x) + g(x)
Thus, we have;
(f + g) (x) = |2x +1| + 3 + (-2)
= |2x +1| + 3 - 2
= |2x +1| + 1
Thus, the solution to (f + g) (x) is Option B: |2x +1| + 1
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please refer to the image below!!
The expression of f(x) = -2x² - 10 which is h(x) = -2x² - 6 would be vertically upward by 3 units, it becomes the graph of a function for f(x).
What is a function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
The function h is defined as follows.
h(x) = -2x² - 6
If the graph of his translated vertically upward by 3 units, it becomes the graph of a function for f(x)
To determine the expression for f(x).
Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.
For example, If shift up by 1 unit, add 1 to the function
If shift down by 4 units, subtract 4 from the function
Here h + 4 because adding 2 to the h coordinate would shift it up 2
⇒ h(f(x)) = ( x, y +4 )
⇒ f(x) + 4 = -2x² - 6
⇒ f(x) = -2x² - 6 -4
⇒ f(x) = -2x² - 10
Hence, the expression of f(x) = -2x² - 10 which is h(x) = -2x² - 6 would be vertically upward by 3 units, it becomes the graph of a function for f(x).
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Use the Distributive Property to write 2(-3 + 9) as an equivalent expression. Then evaluate.
O 2(12); 24
O2(-3) + 2(9); 24
O 2(-3) + 2(9); 12
(3 + 9)2; 24
Sachin can drive 110 more miles before he has to get gas.He has to drive 67 miles to his friends house and 32 miles to his moms.Use rounding to estimate whether he will have enough gas to go to both places
Rounding to an estimate, Sachin will have enough gas to go to both places before he runs out of gas.
What is an estimate?An estimate is an equivalent numerical value obtained by rounding off.
The result of an estimate is not an exact value. The value represents the nearest rounded value.
For instance, 75.9% can be estimated or rounded off to 76%. 32 minutes can be rounded off or approximated to ¹/₂ hour.
Data and Calculations:Driving distance before getting gas = 110 miles
The distance to his friend's house = 67 miles
The distance to his mom's house = 32 miles
The total distance to be covered on the available gas = 99 miles
Estimated distance to be covered = < 100 miles
Thus, using estimation, Sachin will still have more than 10 miles to drive before he gets gas.
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What value of x makes this equation true?
x/2 − 6 = 10
Drag and drop the number that correctly completes the equation.
x = blank
30 31 32 33 34
The table shows information about the masses of some dogs.
a) Work out the minimum number of dogs that could have a mass of more than 24 kg.
b) Work out the maximum number of dogs that could have a mass of more than 24 kg.
a) A minimum of number of dogs that could have a mass of more than 24 kg is 6.
b) The maximum number of dogs that could have a mass of more than 18 kg is 20.
What do minimum and maximum value mean?Rearrange the function using fundamental algebraic concepts to get the value of x when the derivative equals 0. This response gives the x-coordinate of the function's vertex, which is where the maximum or minimum will occur. To find the minimum or maximum, rewrite the solution into the original function.
The minimum of the values present in the interval 20 to 40 is 6
The maximum of the values present in the interval 20 to 40 is (12+6) = 18
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455 times 6 step by step
Answer: 2,730
Step-by-step explanation:
Explained in mental math proccess:
In 455, the one value will be multiplied by 6. 5x6= 30.
In 455, the tens value will be multiplied by 6. 50x6= 300.
In 455, the hundreds value will be multipled by 6. 400x6= 2,400.
Find the sums of all products multiplied by 6. 30+300+2,400= 2,730.
455x6= 2,700
Work out 10.3% of 853.93km
Give your answer rounded to 2 DP.
Answer: 87.96 km
Step-by-step explanation:
10.3% of 853.93km= 87.96 km
Find the product.
654
×
42
=
□
A.
3
,
600
B.
3
,
824
C.
25
,
268
D.
27
,
468
Answer:
D. 27,468
Step-by-step explanation:
654
x42
--------
1,308
+26,160
---------
27,468
DETERMINE WHETHER THE LINES ARE PARALLEL, PERPENDICULAR, OR NEITHER
5X+2y=14 AND y=-5x+9
The lines are neither, nor perpendicular
How to determine the relationship?The equations of the lines are given as
5x + 2y = 14
y = -5x + 9
Make y the subject in both equations
So, we have
y = -2.5x + 7
y = -5x + 9
The slopes of the above equations are
m1 = -2.5
m2 = -5
The above slopes are neither equal not opposite reciprocals
Hence, the lines are neither, nor perpendicular
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Consider the system of linear equations.
−4x+6y = 4
2x−3y = k
Determine the constant so that the system of linear equations has infinitely many solutions. (Hint: Graph the equations in the same coordinate plane. What should you see in order for the system to have infinitely many solutions?)
The value of the constant k such that the system has infinitely many solutions is; -2.
What is the value of k such that the system has infinitely many solutions?It follows from the task content that the system of equations given upon observation are multiples.
Hence, by multiplying the second equation by -2; we have;
-4x +6y = 4
-4x +6y = -2k
Hence, for the system to have infinitely many solutions; 4 = -2k.
Ultimately, k = -2 by dividing both sides of the equation above by -2.
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A car dealership sells SUVs and passenger cars. For a recent year, 30 more SUVs were sold than passenger cars. If a total of 540 vehicles were sold, determine the number of each type of vehicle sold.
The number of each type of vehicle sold are :
SUVs : 300
Passenger cars : 270
Number of SUVs were sold more than passenger cars = 30
Total number of cars sold = 540
Let the number of Passenger car sold = x
Then, The number of SUVs sold = x + 30
So, Total number of cars sold = Number of Passenger car sold + Number of SUVs sold
540 = x + (x + 30)
2x + 30 = 540
2x = 540
x = 540/2
x = 270
We got, the number of Passenger car sold (x) = 270
The number of SUV's sold = x + 30
The number of SUV's sold = 270 + 30 = 300
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solve the following equation for d. 4hd=3f-g3
The equation solved for 'd' gives d = 3f - g³/ 4h
What is subject of formula?
The subject of a formula is defined as the variable expressed in terms of the other variables.
It is also the variable that is worked out in a given equation or expression;
Given the equation;
4hd = 3f - g³
To solve for 'd'
Divide both sides by the coefficients of d, we have;
4hd/ 4h = 3f - g³/ 4h
We then have
d = 3f - g³/ 4h
Thus, the equation solved for 'd' gives d = 3f - g³/ 4h
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Question 2
For all rational numbers a and b, a−b = a + (−b).
O True
O False
It is true. For all rational numbers a and b, a−b = a + (−b).
Given that,
To determine whether the statement, "For all rational numbers a and b, a−b = a + (−b)." is true or false.
In mathematics, a rational number is a number that can be described as the result of a fraction of value or does not have face value.
Here,
= a + (-b)
Since in the parenthesis there is a negative value, when we open the parenthesis the sign of the arithmetic operator will change accordingly,
So,
= a - b
So, the condition is true for all rational numbers.
Thus, It is true. For all rational numbers a and b, a−b = a + (−b).
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1.1.2 Show how the catering cost was determined if the cost per person is R225,00.
The catering cost was determined if the cost per person is R225,00. then the cost of 50 people is equal to = 1,125,000 R.
The catering cost was determined if the cost per person is R 225,00.
The cost per person = 225,00 R
To calculate the cost per unit, add all of your fixed costs and all of your variable costs together and then divide this by the total amount of units you produced during that time period.
Let us assume,
Suppose you can find the cost for 50 people.
Then,
We can write,
Catering cost = x
x = 225,00 * 50
x = 1,125,000 R
Therefore,
The catering cost was determined if the cost per person is R225,00. then the cost of 50 people is equal to = 1,125,000 R.
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the circumference of earth is approximately 2.49x10^4 miles. If Philip traveled around the circumference of Earth 20 times, what would the approximate number of miles he traveled
The approximate no . of miles Philip traveled are 4 . 98 * ( 10 ^ 5 ) miles .
Given : the circumference of earth 2.49 x ( 10^4 ) miles
To calculate : the approximate number of miles Philip traveled
Philip traveled 20 times
⇒ 20 * circumference of circle
⇒ 20 * [ 2.49 x ( 10^4 ) ]
( 2 * 2.49 ) * ( 10 ^ 5 )
= 4 . 98 * ( 10 ^ 5 )
Hence , the approximate no . of miles Philip traveled are 4 . 98 * ( 10 ^ 5 ) miles .
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help me with this question
Answer:3
Step-by-step explanation:
In 1995, the standard bus fare in a city was $1. In 2022, the standard bus fare was $2.25. Find the percent
increase. (Round to the nearest tenth of a percent.)
Answer:
Submit Question
Express each fraction as an expression using a negative exponent organ than -1.
1/25=?
Answer:
A negative exponent flips the fraction and turns the exponent positive, and vice versa.
1/121 = 1/1211 = 121-1
As an example, 5-2 = 1/25, and 1/5-2 = 25.
Evaluate x²-5xy for x = -3 and y = -2
Answer: -21
Step-by-step explanation:
x = -3 and y = -2
x²-5xy=
(-3)²-5(-3)(-2)=
9-5(-(-6))=
9-5(6)=
9-30=
-(30-9)=-21
If COS theta =2√2/4, calculate the value of Sin theta
Answer: [tex]\frac{1}{\sqrt{2}}[/tex]
Step By Step Explanation:
[tex]=\frac{2\sqrt{2}}{2\cdot \:2}[/tex]
[tex]=\frac{\sqrt{2}}{2}[/tex]
[tex]=\frac{\sqrt{2}}{\sqrt{2}\sqrt{2}}[/tex]
[tex]=\frac{1}{\sqrt{2}}[/tex]
What is the equation?
Answer:
Answer = (2)n+(2)
Step-by-step explanation:
As the first step try to examine the distribution on both sides carefully.And as a general rule of thumb, try calculating the difference between 2 consecutive terms on "OUT" side. (if the difference is the same for every 2 consecutive terms, then the distribution is arithmetic)In this case it is (-4) - (-2) = -2.After that, try writing the first OUT term in terms of both that difference (most of the time difference comes in multiplication with n) and the first term on IN side.If that cannot be achieved in one go, then either add or subtract a suitable amount of value. it is as follows,first difference = -2
Now, -2 = -2 × (n) + (0) if n = 1
or -2 = -2 × (n) + (-6) if n = -2
or -2 = |-2| ×(n) + 2 :::: -2 = 2n +2 if n = -2
Now all the 3 arrangements are okay but except for the third one, others do not comply with higher terms in the distribution.Therefore, the third one turns out to be the correct arrangement.Your yard is a mess, and you decide to hire a landscaper. The greenhouse charges a $20 consultation fee plus $11 per hour for the actual work. Garden pros does not charge a consulting fee, but charges $15 per hour for the actual work. Write an equation that will help you determine the # of hours at which the 2 companies charge the same. Clearly indicate what the variable represents.
Answer:
5 hoursStep-by-step explanation:
Let the hours of actual work be x and total charge be y.
The greenhouseTotal amount of charge is:
y = 11x + 20Garden prosTotal amount of charge is:
y = 15xSince y is same for both companies, set the equation and solve for x:
11x + 20 = 15x15x - 11x = 204x = 20x = 20/4x = 5The formula to convert Celsius to Fahrenheit is F=9/5c+32. Convert 45F- to Celsius. Round to the nearest degree. O A. 49°C O B. 7°C O C. -1°C O D. 113°C
>
Suppose you want to have $300,000 for retirement in 35 years. Your account earns 10% Interest.
How much would you need to deposit in the account each month?
Answer: 79.02
Step-by-step explanation:
set present value to 0
set future value to 300000
set number of time periods to 35 * 12 = 420
set interest rate percent per time period to 10/12 = 0.833333.
Equation:
See attachment
the dimensions of a rectangle are 2x-3 and 5x+1. what is the area in sqaure feet
The area of the rectangle is 10x² - 13x - 3.
How to calculate the area?It should be noted that the area of a rectangle is the length multiplied by the width.
Here, the dimensions of a rectangle are 2x-3 and 5x+1.
The area will be:
= (2x - 3)(5x + 1)
= 10x² + 2x - 15x - 3
= 10x² - 13x - 3
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In a lab experiment, 5300 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 10 hours. How many bacteria would there be after 12 hours, to the nearest whole number?
There will be roughly 12,000 bacteria after 12 hours.
What are mathematical operations?A mathematical "operation" is the process of calculating a value using operands and a math operator. The math operator symbol contains predefined rules that must be applied to the given operands or numbers. A mathematical expression is a collection of numbers and operations.So, there are 5300 bacteria and it gets doubles in 10 hours:
Then,
5300 + 5300 = 10,600 (In 10 hours)5300 × 1/5 = 1060 (In 2 hours)In 12 hours = 10,600 + 1060 = 11,660After rounding off: 12,000Therefore, there will be roughly 12,000 bacteria after 12 hours.
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A long year-end status report for work is 130 pages long. You need to print 17 copies for a meeting next week. How much is the paper going to cost for those reports? Paper is sold in reams (500 pages) for $3.44 each. S Give your answer to the nearest cent, only for the paper you use
Answer:
$17.20
Step-by-step explanation:
You need to print (130)(17) = 2210 pages.
This means you need 2210/500 reams, which rounds up to 5.
So, the cost is 5(3.44) = $17.20
Answer:
7602.40
Step-by-step explanation:
Based on the given conditions
Formulate:
3.44×30×17
447.2×17
7602.4
Round 7062.4
=7062.40
2. What does it mean if P(-4) for the polynomial function P(x) = x3 + 11x²
+34x + 24 equals zero?
Answer:
It means that the -4 is one of the solutions for this polynomial. In other words, -4 is a point in the x axis of the graph where the function touches said axis.
The value of the polynomial at P(-4) will be 0.
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Given that the polynomial function is P(x) = x³ + 11x² + 34x + 24. The value of the function at P(-4) will be calculated as:-
P(x) = x³ + 11x² + 34x + 24
P(-4) = (-4)³ + 11(-4)² + 34(-4) + 24
P(-4) = -64 + 176 - 136 + 24
P(-4) = 200 - 200
P(-4) = 0
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write an equation for the line that passes through (-4,-4) and (8,5)
Answer:
The equation for this line is (P(x,y)----> P'(2h-x,2k-y), hence h=3 and k=1/2
Step-by-step explanation:
P(x,y)----> P'(2h-x,2k-y)
P(-4,-4)---->P'(8,5)
Now comparing the corresponding sides;
2h+4=8
2h=8-4
2h=4
h=2
Again,
2k-y=5
2k+4=5
2k=5-4
2k=1
k=1/2
Now, checking the answer:
P(-4,-4)----->P'{2*2-(-4),2*1/2-(-4)}
=P'(4+4,1+4)
=P'(8,5)
ACME movers charges $59 plus $20 per hour to move household goods across town. Hank movers charges$45 per hour. For what length of time does it cost less to
The length of time that it cost less to move good across town will be more than 2.36 hours.
How to explain the information?From the information, ACME movers charges $59 plus $20 per hour to move household goods across town and Hank movers charges $45 per hour.
Let the number of hours be represented by h.
Therefore, the appropriate equation will be:
59 + 20h = 45h
Collect like terms
45h - 20h = 59
25h = 59
h = 59/25
h = 2.36 hours.
Therefore, the length of time that it cost less to move good across town will be more than 2.36 hours.
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ACME movers charges $59 plus $20 per hour to move household goods across town. Hank movers charges $45 per hour. For what length of time does it cost less to move good across town?
