The value of the following composite function is as follows:
(f + g)(-2) = 5(f - g)(-2) = - 5(fg)(-2) = 18(f/g)(-2) = 2How to solve composite function?The composite functions can be solved as follows:
Therefore, the given function are:
f(x) = x² - x
g(x) = 3x + 9
Hence,
a.
(f + g)(-2) = f(-2) + g(-2)
f(-2) + g(-2) = (2)² - 2 + 3(-2) + 9
f(-2) + g(-2) = 4 - 2 - 6 + 9
f(-2) + g(-2) = 5
Therefore, the function (f + g)(-2) = 5
b.
(f - g)(-2) = f(-2) - g(-2)
f(-2) - g(-2) = (2)² - 2 - (3(-2) + 9)
f(-2) - g(-2) = 4 - 2 - 3
f(-2) - g(-2) = -5
Therefore, the function (f - g)(-2) = - 5
c.
(fg)(-2)= f(-2) × g(-2)
f(-2) × g(-2) = (-2)² - (-2) × 3(-2) + 9
f(-2) × g(-2) = 4 + 2 × 3
f(-2) × g(-2) = 6 × 3
f(-2) × g(-2) = 18
Therefore, the function (fg)(-2) = 18
d.
(f/g)(-2) = f(-2) / g(-2)
f(-2) / g(-2) = -2² - -2 / 3(-2) + 9
f(-2) / g(-2) = 6 / 3
f(-2) / g(-2) = 2
Therefore, the function (f/g)(-2) = 2
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If figure, angle ABE & angle DBC are right angles. Prove that angle ABD ≊ angle EBC
Hurry and answer please
Angle ABE & angle DBC are right angles then ∠ABE≅ ∠EBC
What is complementary angle theorem?
If two angles are complementary to the same angle, then they are congruent.
1.∠ABE and ∠DBC are right angles(Given)
2. m∠ABE=90⁰
m∠DBC=90⁰
By definition of right angles
3.∠ABE and ∠DBE are complementary.
∠DBE and ∠EBC are complementary.
(By complementary theorem)
two angles are complementary to the same angle, then they are congruent.
4. ∠ABE≅ ∠EBC (is complementary to same)
Hence ∠ABE≅ ∠EBC.
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PLS HELP WILL MARK BRAINLIEST
Answer:/Step-by-step explanation:
10. Write the phrase "20 divided by x minus 3 is 12" as a variable expression.
20
---------- = 12
x - 3
11. Write the phrase "4 plus the quotient of 9 and y equals 6" as a variable expression.
4 + (9 ÷ y) = 6
I hope this helps!
what the slope of the following equations y y equals -1/2x+4
the form or the slope-intercept form of the equation of the line is
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept
we have the next equation
[tex]y=-\frac{1}{2}x+4[/tex]as we can see the slope is m=-1/2, because we have the same form of the slope-intercept form
determine the maximum or minimum of the quadratic function. express your answer in the form (x,y) and using decimals rounded to the hundredths.f(x)=2x^2+7-10
We are given the following quadratic equation
[tex]f(x)=2x^2+7x-10[/tex]The vertex is the maximum/minimum point of the quadratic equation.
The x-coordinate of the vertex is given by
[tex]h=-\frac{b}{2a}[/tex]Comparing the given equation with the general form of the quadratic equation, the coefficients are
a = 2
b = 7
c = -10
[tex]h=-\frac{b}{2a}=-\frac{7}{2(2)}=-\frac{7}{4}=-1.75[/tex]The y-coordinate of the vertex is given by
[tex]\begin{gathered} f(x)=2x^2+7x-10 \\ f(-1.75)=2(-1.75)^2+7(-1.75)-10 \\ f(-1.75)=2(3.0625)^{}-12.25-10 \\ f(-1.75)=6.125^{}-12.25-10 \\ f\mleft(-1.75\mright)=-16.13 \end{gathered}[/tex]This means that we have a minimum point.
Therefore, the minimum point of the given quadratic equation is
[tex](-1.75,-16.13)[/tex]Answer:
Exact Form:x=±√6/2
Decimal Form:x=1.22474487,−1.22474487
Step-by-step explanation:
Please help
12x2+20-3x−5
Factor out the GCF from the entire expression
I WILL FIRST GROUP THE LIKE TERMS AND SIMPLIFY THEM BEFORE FACTORISING
IT IS VITAL TO SIMPLIFY LIKE TERMS BEFORE FACTORISING.
[tex]12 {x}^{2} - 3x + 20 - 5 \\ = 12 {x}^{2} - 3x + 15[/tex]
THE GCF IN THE EXPRESSION IS 3 MEANING WE WILL DIVIDE EACH AND EVERY TERM IN THE P
EXPRESSION BY 3
[tex] = 3(4 {x}^{2} - x + 5)[/tex]
HOPE THIS HELPS.
MotoWin Auto Superstore is thinking about offering a two-year limited warranty for $928 on all new cars of a certain model. The terms of the warranty would be that MotoWin would replace the car free of charge under certain, specified conditions. Replacing the car in this way would cost MotoWin 13,800 . Suppose that under the warranty, there is a 7% chance that MotoWin would have to replace the car one time and a 93% chance they wouldn't have to replace the car.
MotoWin can expected to make money from offering these warranties.
In the long-run, they should expect to make 514 dollars from each warranty sold
What is expected value of replacement?
The expected value to MotoWin Auto Superstore of a replacing a car is the sum of the costs to be incurred when there is replacement multiplied by its probability of occurrence plus the cost of no replacement multiplied by its likelihood of occurrence expressed in percentage terms
expected value of replacement=(cost of replacement*its probability)*(cost of no replacement*its probability)
cost of replacement=$13,800
probability of replacement=7%
cost of no replacement=$0(when there is no to replace no cost is incurred)
probability of no replacement=93%
expected value of replacement=($13,800*3%)+($0*97%)
expected value of replacement=$414
profit on replacement=replacement price-expected value of replacement
profit on replacement=$928-$414
profit on replacement=$514
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of lines with the following characterizing property. (h) mar + 2) = -1 (b) perpendicular to 3r + 2y = 7 (d) having inclination 60° (f) passing through the origin (h) having slope 6) x-intercept twice y-intercept
We need to write the equation of the family of the lines with the following characterizing property.
j) x - intercept is twice y - intercept
X- intercept is the value of x when y= 0
Y- intercept is the value of y when x = 0
so, let y- intercept = a
x- intercept = twice y- intercept = 2a
So, the line will pass through the points: ( 2a , 0 ) and ( 0 , a )
The general equation of the line is : y = m * x + b
Where m is the slope and b is y - intercept
[tex]slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{a-0}{0-2a}=\frac{a}{-2a}=-\frac{1}{2}[/tex]So, the equation of the family will be :
[tex]y=-\frac{1}{2}x+a[/tex]The graph shows the function f(x).
f(x)
Which equation represents f(x)?
a.f(x) = -√√x
b. f(x) = -√√x-1
c. f(x)=√√/-x-1
d. f(x)=√x
Answer:
The correct option is 3.
Step-by-step explanation:
The parent cube root function is
From the given graph it is clear that the graph of f(x) is transformed by reflecting the graph of g(x) across y-axis and shifting two units down.
If the parent cube root function is reflected across the y-axis, then x is replaced by -x.
Now, the graph of new function sifts 1 unit down. So, the required function is
The graph shows the function .
From the given graph it is clear that the graph passes through the points (-8,1), (0,-1) and (8,-3).
Check the above function by these points.
At x=-8,
At x=0,
At x=8,
All these points satisfy by the abobe function. It means the above function is correct.
Therefore the correct option is 3.
Please help me with this question my son keeps getting this wrong, please help I have attached the image of the problem from his math paper.
The terms in the given expression are
[tex]8x^3y^2,4x^2y^3,40xy^3[/tex]The common factor in all the three time is
[tex]4xy^2[/tex]Take the common factor outside the brackets and write the remaining inside the brackets.
[tex]4xy^2(2x^2-xy+10y)[/tex]Find the sum and product of the roots of the equation 4x^2-12=3x
Given the equation:
[tex]4x^2-12=3x\text{ ----- equation 1}[/tex]Required: sum and product of the roots of the equation
solution:
For a quadratic equation of the form
[tex]ax^2\text{ + bx + c = 0 ------ equation 2}[/tex]the sum of the roots is expressed as
[tex]\text{sum of roots = -}\frac{b}{a}[/tex]the product of the roots is expressed as
[tex]\text{product of roots = }\frac{c}{a}[/tex]The given quadratic equation can be rewritten in the form as in equation 2 to be
[tex]4x^2-3x-12\text{ = 0 ----- equation 3}[/tex]In comparison to equation 2,
[tex]\begin{gathered} a\text{ = 4} \\ b\text{ = -3} \\ c\text{ =-12} \end{gathered}[/tex]Thus,
Sum of roots:
[tex]\begin{gathered} \text{sum of roots = -}\frac{b}{a} \\ =-\frac{-3}{4} \\ =\frac{3}{4} \end{gathered}[/tex]thus, the sum of the roots is
[tex]\frac{3}{4}[/tex]Products of roots:
[tex]\begin{gathered} \text{product of roots = }\frac{c}{a} \\ =\frac{-12}{4} \\ =-3 \end{gathered}[/tex]thus, the product of the roots is
[tex]-3[/tex]
what’s the correct answer answer asap for brain list
Answer:
B is the correct answer
hope this helped:)
last monday two law students met up at Cafe literature after school to read the pages they were assigned in the legal methods class Alejandro can read one page per minute and he has 28 pages so far Carly who has a reading speed of two pages per minute has read 12 pages so far.Write an equation to describe the pages each student read.Graph the equations.Which are the ratios for each student?
Let x be the number of minutes they read and y the number of pages they read.
Since Alejandro read one page per minute and he has so far read a total of 28 pages he the total amount of pages he read is:
[tex]y=x+28[/tex]Now, Carly reads twice as much in the same time but she has read only 12 pages so far, then the amount of pages in her case is:
[tex]y=2x+12[/tex]The graphf of this equations are:
The rate of change:
Alejandro: 1
Carly: 2
Please Help, thank you.
The interval notation for the change in temperature are-
Increasing temperature; (1, 3) ∪ (6, 8).Decreasing temperature; (0, 1) ∪ (3, 6).What is termed as the interval notation?An interval is represented on a number line using interval notation. In those other words, it is a method of writing real number line subsets. An interval is made up of numbers that fall between two particular given numbers.For the given function;
Increasing temperature; It is the temperature in which the graph is increasing or we can say that for as the vale of x increases the value of y also increases. Thus, the interval notations are-
Increasing temperature; (1, 3) ∪ (6, 8).
Decreasing temperature: It is the temperature in which the graph is decreasing or we can say that for as the vale of x increases the value of y also decreases. Thus, the interval notations are-
Decreasing temperature; (0, 1) ∪ (3, 6).
Thus, the interval notations for the function are found.
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Mia Kaminsky sells shoes for Macy’s. Macy’s pays Mia $12 per hour plus a 5% commission on all sales. Assume Mia works 37 hours for the week and has $7,000 in sales. What is Mia’s gross pay
Mia's gross pay was $794 at the end of the week.
Mia's Gross PayTo calculate Mia's gross pay, we have to find how much she earned working 37 hours at a rate of $12 per hour.
Total number of hours worked = 37Rate per hour = $12We can simply multiply both variable to determine how much she earned working for 37 hours.
[tex]37 * 12 = 444[/tex]
Mia earned $444 for that week.
We can add this to her 5% commission which would be 5% of $7000
[tex]5\% of 7000 = 350[/tex]
The sum of Mia's gross pay for the week is
[tex]444 + 350 = 794[/tex]
She earned $794 in gross pay at the end of the week.
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Hello! I need some help with this homework question, please? The question is posted in the image below. Q3
As given by the question
There are given that the function:
[tex]f(x)=x^2+3[/tex]Now,
From the given formula:
[tex]\frac{f(x+h)-f(x)}{h}[/tex]Then,
First find the equation for f(x + h)
So,
[tex]\begin{gathered} f(x)=x^2+3 \\ f(x+h)=(x+h^{})^2+3 \\ f(x+h)=x^2+h^2+2xh+3 \end{gathered}[/tex]Then,
Put both values into the given formula:
So,
[tex]\frac{f(x+h)-f(x)}{h}=\frac{x^2+h^2+2xh+3-x^2-3}{h}[/tex]Then,
[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{h^2+2xh}{h} \\ =\frac{h(h^{}+2x)}{h} \\ =h+2x \\ =2x+h \end{gathered}[/tex]Hence, the difference quotient is 2x + h.
f(a)=-3a-5; Find ƒ(-7)
Step-by-step explanation:
the answer is attached
hope it helps
mark the red letter shown in the brackets the subject of the formula
Given equation is
[tex]A=lb[/tex]Now
[tex]b=\frac{A}{l}[/tex]Compare and contrast the formulas for calculating the volume of a cone and the volume of apyramid. Give a mathematical example to illustrate your discussion.
SOLUTION:
Step 1:
In this question, we are given the following:
Compare and contrast the formulas for calculating the volume of a cone and the volume of a pyramid.
Give a mathematical example to illustrate your discussion.
Step 2:
The details of the solution are as follows:
The formula for calculating the volume of a cone:
The formula for calculating the volume of the pyramid:
I only need the answer
THANK YOU!!
After simplifying the expression to a singles complex number, it becomes 1+√3i.
A complex number is a unique kind of number in the number system, it has two parts. One it called the real part which is a real number and an imaginary part which is also a real part but accompanied by the specific notation called iota.
Here a complex number Z is provided to us,
Z = [2+√(-12)]/2
As we can see,
Here we have √-12
We can write it as,
√(-2×2×3)
= 2√(-3)
Here, √-1 is given that special notation "IOTA (i)" which we mentioned earlier.
=2√3i
So, Z becomes,
Z = (2+2√3i)/2
Z= 1+√3i
So, the simpler form of Z = [2+√(-12)]/2 is Z= 1+√3i.
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Find the domain of the rational expression: 3x+21
all real numbers except 4
all real numbers except -7
all real numbers except 0
all real numbers except -21
Answer: The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Domain: (−∞,∞)
Range: (−∞,∞)
Hope this helps! :)
Find the maximum value of
C = x + 4y
subject to the following constraints:
x ≥ 0
x≤ 12
y ≤ 10
2x + 3y ≥ 24
The maximum value of the linear equation is obtained as 52.
What is termed as the maximum value of function?The maximum value of such a function is the point on a graph where the function achieved its maximum point, or vertex.There are several ways to find the maximum value of the a quadratic equation.The first method is graphing. Visually, you can determine the highest value by graphing the equation and locating the maximum point of the graph. This is especially simple if you have a graphing calculator. There are three ways to calculate the maximum value of the a quadratic equation. Each of them can be employed to ascertain the maximum in their own specific context.For the given question;
The linear equation is defined as;
C = x + 4y
The constraints are-
x ≥ 0
x≤ 12
y ≤ 10
2x + 3y ≥ 24
From the constraints, the maximum value for x and y are taken as;
x = 12 and y = 10.
Put the the equation, to find the maximum value.
C = x + 4y
C = 12 + 4×10
C = 52
Thus, the maximum value of the function is obtained as 52.
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Which is an algebraic expression for five more than z
The algebraic expression for 5 more than z is Z + 5.
Given,
5 more than z.
We need to find the algebraic expression.
What are the different algebraic expressions?
We have,
Examples:
- 3 more than M = M + 3
- 3 less than M = M - 3
- 3 times M = 3 x M
- 3 times M less than 2 = 3M - 2
- 3 times M more than 2 = 3M + 2
Find the algebraic expression for 5 more than Z.
We have,
5 more than Z = Z + 5
Thus the algebraic expression for 5 more than z is Z + 5.
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Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms. Third-degree, with zeros of -3,-2, and 1, and a y-intercept of -14.
Recall that the general form of a third-degree polynomial is:
[tex]g(x)=k(x-a)(x-b)(x-c),[/tex]where k is a constant, and a, b, and c are the zeros of the polynomial.
Therefore:
[tex]p(x)=k(x+3)(x+2)(x-1).[/tex]Now, to determine the value of k, we consider the y-intercept:
[tex]p(0)=-14=k(0+3)(0+2)(0-1).[/tex]Solving for k, we get:
[tex]\begin{gathered} -14=-6k, \\ k=-\frac{14}{-6}, \\ k=\frac{14}{6}, \\ k=\frac{7}{3}. \end{gathered}[/tex]Finally:
[tex]p(x)=\frac{7}{3}(x+3)(x+2)(x-1).[/tex]Answer: [tex]p(x)=\frac{7}{3}(x+3)(x+2)(x-1).[/tex]Marian purchased a home valued at $465,000. She purchased homeowner insurance for 75% of the value of the home. If the annual premium on the policy was $0.74 perhundred-dollar unit, how much did she pay to the nearest whole cent)?$2,875.50$2,695.00$2,580.75$3,050.74None of these choices are correct.
The value of the police if fot the 75% of the total value of the home value. The 75% of $465000 is:
[tex]465000\cdot0.75=348750[/tex]The value of the insurance is then for $348750. The annual premium of the policy is $0.74 per hunder-dollar unit. Then, we need to estimate the hundred-dollar units in $348750. To estimate them, we need to divide the value by 100:
[tex]\frac{348750}{100}=3487.5[/tex]The value of the policy is then by 3487.5 hundreds of dollars. Now, we can estimate the amount to be paid yearly:
[tex]0.74\cdot3487.5=2580.75[/tex]Then, the amount to pay, according to the given conditions is $2580.75. Correct answer is the third option.
Find all real values of x such that f(x)=0 for f(x) = 2x^2 + 3x – 20
Consider first the general case of the equation
[tex]ax^2+bx+c\text{ =0}[/tex]The general formula that solves this problem is given by
[tex]x\text{ = }\frac{-b\text{ }\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case, the number of real solutions depends on the value that is inside the square root. For it to have a real value, it must happen that
[tex]b^2-4ac\ge0[/tex]So first, let's check if this is our case. In our case a = 2, b = 3 and c = -20.
Then
[tex]b^2-4ac=(3)^2-4\cdot2\cdot(-20)\text{ = 9 +160 = }169\ge0[/tex]So in this case, the equation has real values. Now, recall that
[tex]169=13^2[/tex]So our general solution becomes
[tex]x\text{ = }\frac{-3\pm\sqrt[]{13^2}}{2\cdot2}[/tex]Then,
[tex]x\text{ = }\frac{-3\text{ }\pm\text{ 13}}{4}[/tex]The symbol in the middle means that we get one different solution whenever we take either the plus sign of the minus sign. So the first solution would be
[tex]x_{1\text{ }}=\frac{13-3}{4}\text{ = }\frac{10}{4}\text{ = }\frac{5}{2}[/tex]And the other solution would be
[tex]x_{2\text{ }}=\text{ }\frac{13+3}{4}\text{ = }\frac{16}{4}=4[/tex]
I am having a hard time understanding explicit formulas with arithmetic sequences. The current sequence I am working with is:2, 8, 14, 20, 26The common difference is 6. I don't know how to come up with the explicit formula when given the sequence.
Solution
we are given the sequence
[tex]2,8,14,20,26,..[/tex]The first term = 2
Common difference = 6
The sequence is an arithmetic progression
The nth term is given as
[tex]\begin{gathered} a_n=a+(n-1)d \\ a=2 \\ d=6 \\ a_n=2+(n-1)(6) \\ a_n=2+6n-6 \\ a_n=6n-4 \end{gathered}[/tex]Therefore, the answer is
[tex]a_{n}=6n-4[/tex]Simplify −6g(3g + 2).
−18g^2 + 2
−18g^2 − 12g
−18g + 2
−18g − 12g
Answer:
B. −18g^2 − 12g
Step-by-step explanation:
Hope this helps!
Please tell me if its incorrect
When Mr. Jackson got in his car yesterday, the odometer read 187,198.9 km. When he got home, the reading was 187,399.4 km. How far did Mr. Jackson drive?
The distance Mr. Jackson drove from when he got in his car to when he got home is 200.5 km.
Given:
The odometer reading when Mr.Jackson got in his car = 187,198.9 km
The odometer reading when Mr.Jackson got home = 187,399.4 km
An odometer is a device used to calculate the distance traveled by a vehicle.
To determine the distance Mr.Jackson drove we subtract the odometer readings from when he got home minus when he got into his car.
⇒ (187,399.4 - 187,198.9) km
⇒ 200.5 km
Therefore, Mr. Jackson drove 220.5 km from when he got in his car to when he got home.
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*THIS IS AN ANSWER BECAUSE I CAN'T ANSWER SOMEONE'S QUESTION*
Bob can do a job in 5 hours, while Bill can do the same job in 8 hours. How many hours would it take them, working together, to do this job?
ANSWER:
The one in the following equation stands for ONE WHOLE JOB.
[tex]\frac{1}{5}x+\frac{1}{8}x=1\\\\[/tex]
[tex]x=\frac{40}{13} hours[/tex]
hence, this is the answer.
Answer:
x=40/13
Step-by-step explanation:
tex]\frac{1}{5}x+\frac{1}{8}x=1\\\\[/tex]
[tex]x=\frac{40}{13} hours[/tex]
Find the value of the expression: 12 ÷ 2 + ( 6 − 4 ) 2
Given:
[tex]12\div2+(6-4)2[/tex]Required:
To find the value of the given expression.
Explanation:
Consider the given expression,
[tex]\begin{gathered} 12\div2+(6-4)\times2 \\ =6+(6-4)2 \\ =6+2\times2 \\ =6+4 \\ =10 \end{gathered}[/tex]Final Answer:
The value of the given expression is 10.