What is (f + g)(x)?f(x) = x + 1g(x) = 3x²Write your answer as a polynomial or a rational function in simplest form.
Answers
Given:
f(x) = x + 1
g(x) = 3x²
To find (f + g)(x), sum the like terms of the function.
(f + g)(x) = f(x) + g(x) = x + 1 + 3x²
(f + g)(x) = 3x² + x + 1
Answer: 3x² + x + 1
Related Questions
Write the equation of the line shown in slope-intercept form.у6543212X9 1034-56 78-3 -2 -1-1-2190 Tutorial
Answers
slope of intercept from the equation of line is
[tex]\begin{gathered} y=mx+c \\ \text{where c is the intercept part of y} \\ c=1 \\ l\in e\text{ cuts y-a}\xi s\text{ at 1} \\ so\text{ point (0,1)} \\ and\text{ cut on 2nd place at 3 on x-a}\xi s \\ so\text{ point is (3,0)} \\ slope(m)=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{0-1}{3-0} \\ m=-\frac{1}{3} \\ \text{equation of line is} \\ y=-\frac{1}{3}x+1 \end{gathered}[/tex]what type of function is this? (quadratic or exponential)
Answers
Answer:
exponential
Step-by-step explanation:
The gold bracelet weighs 70 kg. It is made from 76% gold and 24% aluminium. Find themass of gold in bracelet. Also find the mass of aluminium.
Answers
Given:
The gold bracelet weighs 70 kg.
It contains 76% gold and 24% aluminium.
To find:
The mass of gold and aluminium.
Explanation:
The mass of gold will be,
[tex]\frac{76}{100}\times70=53.2kg[/tex]The mass of aluminium will be,
[tex]\frac{24}{100}\times70=16.8kg[/tex]Final answer:
The mass of gold is 53.2kg and the mass of aluminium is 16.8kg.
In the diagram, what is the relationship between segments AC and BC? Explain your answer.
Answers
In the diagram the relationship between AC and BC is that they are the hypotenuse if the right angle triangles ADC and BDC and they are equal
What is a hypotenuse?The longest side in a right triangle is called the hypotenuse. In a right triangle, it is the side opposite the right angle.
The right triangle's hypotenuse is longer than its other two sides
When a perpendicular bisector (CD) bisects a line (in this case AB) the hypotenuse formed in the process are equal
The base and the perpendicular side, are related in accordance with the Pythagoras theorem. The square of the hypotenuse of a right triangle is the sum of the squares of its base and perpendicular side.
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what is the median of 6 5 9 9 6 7 and 6
Answers
Answer:
6
Explanation:
To know the median, we first need to organize the data from least to greatest, so:
5 6 6 6 7 9 9
Then, the median will be the value that is in the middle, so:
5 6 6 6 7 9 9
Therefore, the median is 6 because there are 3 values to the left of 6 and 3 values to the right of 6.
Solve the system of equation algebraically: y = 2x2 - 5x + 10 and y = 2x + 5.
Answers
In order to solve the system of equations, let's equate both values of y and solve for x using the quadratic formula:
[tex]\begin{gathered} 2x^2-5x+10=2x+5\\ \\ 2x^2-5x-2x+10-5=0\\ \\ 2x^2-7x+5=0\\ \\ a=2,b=-7,c=5\\ \\ x=\frac{-b±\sqrt{b^2-4ac}}{2a}\\ \\ x=\frac{7±\sqrt{49-40}}{4}\\ \\ x_1=\frac{7+3}{4}=\frac{10}{4}=\frac{5}{2}\\ \\ x_2=\frac{7-3}{4}=\frac{4}{4}=1 \end{gathered}[/tex]Now, let's calculate the values of y for each value of x:
[tex]\begin{gathered} x=\frac{5}{2}:\\ \\ y=2x+5=5+5=10\\ \\ \\ \\ x=1:\\ \\ y=2x+5=2+5=7 \end{gathered}[/tex]Therefore the solutions are (1, 7) and (5/2, 10).
Correct option: second one.
Pls, answer in a minute. PLS
Answers
Answer: No, It is not a right-angled triangle.
Step-by-step explanation:
Find the length of the last side first. To do this, add AB and BC together, then deduct that sum from the 22 cm circumference of Triangle ABC.
ABC - (AB + BC) ⇒ 22cm - (8cm + 5cm)
22cm - 13cm = 9cm
Since the hypotenuse of a triangle is always its longest side, we can be certain that the side we identified is the hypotenuse. The Pythagorean Theorem can now be used to determine whether the triangle is a right triangle.
Pythagorean Theorem: a² + b² = c², where a and b are legs and c is the hypotenuse. The triangle is a right triangle if a2 + b2 do equal c2.
8² + 5² = 9²
64 + 25 = 81
89 > 81
The triangle is not a right triangle, but since a and b are longer than c, we can conclude that it is obtuse.
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What is the correct answer to this question The options are A. 24B. 44C. 40D. 52
Answers
Given that
There is a square with its side as PQ = 2x + 8 and the perimeter is 96. And we have to find the side PQ of the square.
Explanation -
As it is a square and all the sides of the square are the same.
Since the perimeter is the sum of all the sides and its formula is given as
[tex]Perimeter\text{ of square = 4}\times side[/tex]On substituting the value we have
[tex]\begin{gathered} 96=4\times(2x+8) \\ \frac{96}{4}=2x+8 \\ 24=2x+8 \\ 2x=16 \\ x=8 \\ So,\text{ PQ = 2}\times8+8=16+8=24 \\ PQ=24 \end{gathered}[/tex]So the correct option is A.
Hence, the final answer is 24.Ursula has a cylinder and a cone that have the same height and radius. Which ratio compares the volume of the cone to the volume of the cylinder? О 1 to 3 01 to 2 O 2 to 1 O 3 to 1
Answers
Answer
The ratio of the volume of a cone to that of a cylinder is 1 to 3
Explanation
The volume of a cone is given as
Volume of a cone = ⅓πr²h
The volume of a cylinder is given as
Volume of a cylinder = πr²h
The ratio of the volume of a cone to that of a cylinder is now
Volume of a cone : Volume of a cylinder
⅓πr²h : πr²h
Divide both sides by πr²h and we have
⅓ : 1
Multiply both sides by 3 and we have
1 : 3
Hope this Helps!!!
evaluate the algebraic expression -x^2y^3+2xy^2-3xy when x=2 and y=-1
Answers
Given expression is:
[tex]f(x,y)=-x^2y^3+2xy^2-3xy[/tex]To find the value at x=2and y=-1 put these valuesin given expression:
[tex]\begin{gathered} f(2,-1)=-(2)^2(-1)^3+2(2)(-1)^2-3(2)(-1) \\ f(2,-1)=4+4+6 \\ f(2,-1)=14 \end{gathered}[/tex]So the value of algebric expression at x=2and y=-1 is 14.
A rectangular paperboard measuring 25 in long and 16 in wide has a semicircle cut out of it, as shown below.Find the area of the paperboard that remains. Use the value 3.14 for IT, and do not round your answer. Be sure to include the correct unit in your answer
Answers
To answer this question we will use the following diagram as a reference:
The semicircle's radius is 8in.
Notice that the area of the paperboard that remains is the area of the rectangular paper board minus the area of the semicircle.
The semicircle's area is:
[tex]A_s=\frac{\pi(8in)^2}{2}=\frac{64\pi}{2}in^2=32\pi in^2\approx100.48in^2.[/tex]The rectangle's area is:
[tex]A_r=16in*25in=400in^2.[/tex]Then the area of the paperboard that remains:
[tex]\begin{gathered} A=400in^2-100.48in^2 \\ =299.52in^2. \end{gathered}[/tex]Answer:
[tex]299.52in^2.[/tex]Be Precise Of the number of sixth grade students at a middle school, 120 prefer online magazines over print magazines. Of the number of seventh grade students, 140 prefer online magazines. A student said that this means a greater percent of seventh grade students prefer online magazines than sixth grade students. Is the student correct? Choose the correct statement that uses precise mathematical language to explain. Multiple choice question. cross out A) no; A percent compares the part to the whole. In this case, the only known value is the part. To compare percents, the whole, the total number of sixth grade students and the total number of seventh grade students, must be known. cross out B) yes; A percent compares the part to the part. In this case, both parts are known. The number of sixth grade students who prefer online magazines, 120, can be compared to the number of seventh grade students who prefer online magazines, 140. So, a greater percent of seventh grade students prefer online magazines than sixth grade students. cross out C) no; A percent must always be less than 100. There are 120 sixth grade students who prefer online magazines and 140 seventh grade students who prefer online magazines, and both of these values are greater than 100. So, they cannot be compared as percents. cross out D) yes; A percent compares the part to the whole. In this case, the known values are 120, which is the part, and 140, which is the whole. Because 140 is greater than 120, a greater percent of seventh grade students prefer online magazines than sixth grade students. Need help with this question? Tools are not currently accessible ©2022 McGraw Hill. All Rights Reserved. Privacy CenterOpens in a new window Terms of UseOpens in a new window Minimum Requirements
Answers
No. There are 120 sixth-grade students who prefer online magazines and 140 seventh-grade students who prefer online magazines, and both of these values are greater than 100. So, they cannot be compared as percentages crossed out.
What is a percentage?It is a branch of Mathematics. It is a number or ratio expressed in the form of a fraction. A percentage can be denoted by the symbol %. It is a dimensionless number and it does not have any unit of measurement. The percentage is mainly used in shopping malls for giving discounts on clothes to customers. And the percent is used in salary increments in the company. The percentage is a very easy concept to learn by students or any other person. Percentage plays a key role in our daily life.
The number of students cannot be compared as percentages as the total number of students for both grades are not given.
So, the correct option is (c) No. There are 120 sixth-grade students who prefer online magazines and 140 seventh-grade students who prefer online magazines, and both of these values are greater than 100. So, they cannot be compared as percentages crossed out.
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Jennifer Lopez met her 10 cousins at a family reunion. The number of male cousins (x) is 2 less than the number of female cousins (y). How many (male,female) cousins were there? (not including Jennifer)
Answers
Answer:
Explanation:
Given that Jennifer Lopez has 10 cousins
The number of male cousins is x
The number of female cousins is y
Since x is 2 less than y, we have:
x = y + 2 ...............................................................................(1)
The total number of cousins is 10, we have:
x + y = 10 ..............................................................................(2)
Substituting equation (1) in (2)
(y + 2) + y = 10
y + y + 2 = 10
2y + 2 = 10
Subtract 2 from both sides
2y = 10 - 2
2y = 8
Divide both sides by 2
y = 8/2 = 2
Substitute the value of y into (1)
x = 2
if I had matrix [1 2 0 -1 -3 2 ; 0 0 1 3 -3 1; 0 0 0 1 -1/6 1/2; 0 0 0 0 1 3/11; 0 0 0 0 0 0]. i need to find the general solution of the systemI was given a system of linear equations and told to put it in reduced row echelon form and then find the general solution of the system. I'm not sure how to write each x1 = , x2=
Answers
With the given matrix, the system of equations you have is:
[tex]\begin{gathered} x_1+2x_2-x_4-3x_5=2 \\ x_3+3x_4-3x_5=1 \\ x_4-\frac{1}{6}x_5=\frac{1}{2} \\ x_5=\frac{3}{11} \end{gathered}[/tex]Then, you already know x5=3/11.
Now replace these value in the equation above and solve for x4:
[tex]\begin{gathered} x_4-\frac{1}{6}\cdot\frac{3}{11}=\frac{1}{2}^{} \\ x_4-\frac{3}{66}=\frac{1}{2} \\ x_4-\frac{1}{22}=\frac{1}{2} \\ x_4=\frac{1}{2}+\frac{1}{22} \\ x_4=\frac{22+2}{44}=\frac{24}{44} \\ x_4=\frac{6}{11} \end{gathered}[/tex]Now, replace x4 and x5 into the next above equation:
[tex]\begin{gathered} x_3+3\cdot\frac{6}{11}-3\cdot\frac{3}{11}=1 \\ x_3+\frac{18}{11}-\frac{9}{11}=1 \\ x_3+\frac{9}{11}=1 \\ x_3=1-\frac{9}{11}=\frac{11-9}{11} \\ x_3=\frac{2}{11} \end{gathered}[/tex]Please help it’s prb easy for u !!!!!!!!
Answers
Answer: The square
Step-by-step explanation:
The square has a 90 degree angle which is a right angle. Also all sides have the same length
What is the quotient (x2 + 10x + 9) ÷ (x + 9)? (1 point)
x − 9
x − 1
x + 1
x + 9
Answers
(x2 + 10x + 9) ÷ (x + 9) The quotient is x + 1.
The correct option is (C)
Given,
In the question:
([tex]x^{2}[/tex] + 10x + 9) ÷ (x + 9)
To find the what is the quotient ?
What is the quotient?
The number that is being divided (in this case, 15) is called the dividend, and the number that it is being divided by (in this case, 3) is called the divisor. The result of the division is the quotient.
Now, According to the question:
x + 1
≡[tex]x + 9\sqrt{x^{2}+10x +9 }[/tex]
[tex]x^{2}[/tex] + 9x
- -
-------------------------
x + 9
x + 9
---------------
0
Hence, (x2 + 10x + 9) ÷ (x + 9) The quotient is x + 1.
The correct option is (C) .
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Which expression represents the greatest common factor (GCF) of 20 and 70?
A. 2 x 5
B. 2 x 7
C. 7 x 5
D. 2 x 2 x 5
Answers
Answer:
A. 2 * 5
Step-by-step explanation:
The factors of 20 are: 1, 2, 4, 5, 10, 20
The factors of 70 are: 1, 2, 5, 7, 10, 14, 35, 70
Then the greatest common factor is 10.
2 * 5 = 10
4. From ThursdaySimplify the e2 (p + 4) + 6p
Answers
the given equation is ,
2(p+4) + 6p
now , we solve it
2p + 8 + 6p
8p + 8
So, the answer is 8p + 9.
Please help me I would appreciateeeeeeeeeeeeee
Answers
The value of the variable x in first figure will be 15.
The value of the variable x in second figure will be 20.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
There are two figure is shown in figure.
Now,
In first figure;
The sum of all the interior angle in a triangle is 180°.
So, We can formulate;
⇒ (6x - 10)° + (2x + 20)° + (3x + 5)° = 180°
Solve for x as;
⇒ (6x - 10)° + (2x + 20)° + (3x + 5)° = 180°
⇒ 6x - 10 + 2x + 20 + 3x + 5 = 180°
⇒ 11x + 15 = 180
⇒ 11x = 180 - 15
⇒ 11x = 165
⇒ x = 15
Thus, The value of the variable x in first figure will be 15.
For second figure;
We can formulate by the corresponding angle of the parallel lines as;
⇒ x + 50 = 70
⇒ x = 70 - 50
⇒ x = 20
Thus, The value of the variable x in second figure will be 20.
Therefore,
The value of the variable x in first figure will be 15.
The value of the variable x in second figure will be 20.
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If G¹(x) is the inverse of G(x), what is the value of G¹(G(x))?
Ο A. x
OB. x¹
O C. 1
OD. O
SUBMIT
Answers
The value of G⁻¹(G(x)) is x , So the correct answer among the following options is A) x
What is function?
A function is described as a relationship between a set of inputs and one output for every one of them. Simply described, a function is an association of inputs where each input is coupled to a single, distinct output. Each function has a codomain or range.
What is inverse function?An inverse function, sometimes known as an antI function, is a function that can change into another function. In other words, if any function "f" takes x → y, then the inverse of that function will take y to x. The inverse of a function denoted by "f" or "F" is denoted by "f-1" or "F-1." Not to be mistaken with an exponent or a reciprocal in this case is (-1).
Given, function G(x)
inverse of the given function G⁻¹(x)
Let G(x) = x
Then G⁻¹(x) = x
So value of G⁻¹(G(x)) is,
Put G(x) = x,
Hence, G⁻¹(G(x)) = x
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4. Is 4(2x - 3) < 8(x + 1) always, sometimes, or never true?
Answers
The given inequality is always true for all real numbers.
Given, the inequality is :
4(2x - 3) < 8(x + 1)
Reduce the greatest common factor for both of the sides of the inequality:
2x - 3 < 2(x+1)
Apply Multiplicative distribution law:
2x - 3 < 2x + 3
Rearrange unknown terms to the left of the side of the equation:
2x - 2 < 2 + 3
Combine the like terms:
0 < 2+3
Calculate the sum or the difference.
0 < 5
The solution of the inequality is always true.
Hence we get the solution as the inequality being true to all real numbers.
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What is the domain of the radical function shown on the graph?
y
-10
y=-x-2-4
A.
all real numbers
B. (XIX50)
+10
2
-6
-8
--10-
Answers
Answer:
A
Step-by-step explanation:
the function is in all the graph from left to right
What is the distance between A and B? Round your answer to the nearest tenth. (4 points) A coordinate plane is shown. Point A is located at negative 1, 5, and point B is located at 4, 1. A line segment connects the two points. ?
Answers
The distance between the 2 points A(-1, 5) and B(4, 1) is √41.
What is the distance?Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.The length of the line connecting two places represents the distance between them. Subtracting the different coordinates will reveal the distance if the two points are on the same horizontal or vertical line.So, the diatence between A(-1, 5) and B(4, 1):
Formula: d=√((x2 – x1)² + (y2 – y1)²Now, calculate as follows:
d=√((x2 – x1)² + (y2 – y1)²d=√((4 – (-1))² + (1 – 5)²d=√(5)² + (-4)²d=√25 + 16d=√41Therefore, the distance between the 2 points A(-1, 5) and B(4, 1) is √41.
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Suppose chang places $7000 and an account that pays 2% interest compounded each year. Assume that no withdraws are made from the account.Follow the instructions below. Do not do any rounding
Answers
In general, the compound interest formula is
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ P\rightarrow\text{ initial amount} \\ r\rightarrow\text{ interest rate} \\ n\rightarrow\text{ number of times the interest is applied per period of time \lparen t\rparen} \\ t\rightarrow\text{ years} \end{gathered}[/tex]In our case, since it is not specified how often the interest is compounded, we will assume that n=1; then,
[tex]A=7000(1+\frac{0.02}{1})^{1*t}=7000(1.02)^t[/tex]a) Set t=1
[tex]\begin{gathered} t=1 \\ \Rightarrow A(1)=7000(1.02)^t=7140 \\ \end{gathered}[/tex]The answer to part a) is 7140b) Set t=2,
[tex]A(2)=7000(1.02)^2=7282.8[/tex]The answer to part b) is 7282.8Notice that we are not given the number of times the interest is applied per year; therefore, we had to assume that it compounds 1 time annually.
pleeeeeese help me solve
Answers
Substitution means that the equation which solves for one variable by using the other equation and the values of the variable [tex](x,y)=(29,53)[/tex]
What is substitution?
A strategy for solving systems of equations that includes solving for one variable and using that solution to find the other variable.
Here the given linear equation is
[tex]y=3x-34 \\\\y=2x-5[/tex]
From the equation [tex](1)[/tex] , [tex](2)[/tex], we get
[tex]y-3x=-34 .....(1)\\\y-2x=-5 ......(2)[/tex]
And the graphical representation is of the form:-
In an equation [tex](2)[/tex], we get
[tex]y=2x-5[/tex]
Put the value [tex]y[/tex] in the equation [tex](1)[/tex], and we get
[tex](2x-5)-3x=-34\\2x-5-3x=-34\\-x-5+34=0\\-x+29=0\\x=29[/tex]
Now, substituting the value of [tex]x[/tex] in the equation [tex](2)[/tex], we get
[tex]y=2x-5\\y=2(29)-5\\y=58-5\\y=53[/tex]
Hence, the values are of the form:-
[tex](x,y)=(29,53)[/tex]
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in your own words state the segment addition postulate.
Answers
see the attached figure
the points A, B and C are collinear (the three points lies on the same line)
so
AC=AB+BC ------> by addition segment postulate
the total length is equal to the sum of its parts
Figure 1 and Figure 2 below are congruent. Which angle corresponds to angle L?
Answers
Answer:
angle E
Step-by-step explanation:
Have 109% in geometry
4 g = 16 g= please solve
Answers
To solve for g in the expression 4g=16, we need to follow these steps:
[tex]\begin{gathered} 4g=16 \\ \frac{4}{4}\times g=\frac{16}{4} \\ g=\frac{16}{4}=4 \end{gathered}[/tex]I need an answer pleaseee hurry
It’s geometry
Answers
Answer:
Angle 1: 115 degrees
Angle 2: 72 degrees
Angle 3: 57 degrees
Angle 4: 18 degrees
Angle 5: 122 degrees
Step-by-step explanation:
Note: I won’t be finding the angles in order
Angle 3 plus 33 is a right angle which is 90 degrees
So we subtract
90-33=57
Angle 3: 57 degrees
Now angle 2 can be found because a triangle sum of all three angles is 180 degrees
We know 2 75 degrees and 33 so we can add them
75+33=108
Now subtract from 180
180-108=72
Angle 2 is 72 degrees
we can find angle 1 by first finding the missing angle next to it in the triangle
75+40=115
180-115=65
Now we can subtract 65 from 180 to find angle 1
180-65=115
Angle 1 is 115 degrees
Next to find angle 4 we have to find the other missing angle since we already know angle 3 is 57 degrees
The missing angle we just subtract 75 from 180 since the angles are next to each other on a flat plane
180-75=105
And now we add the 2 angles we know
105+57=162
Now subtract from 180
180-162=18
Angle 4 is 18 degrees
Now angle 4 and angle 5 plus 40 degrees is equal to 180 degrees
To find angle 5 we add 40 degrees and 18
40+18
58
Now subtract from 180
180-58
122
Angle 5 is 122 degrees
Hopes this helps please mark brainliest
EMERGENCY WILL GIVE BRAINLIEST.
GRAPH Y=1/2X FOR ME PLEASE!
ON A COORDINATE PLANE
Answers
The graph of y = 1/2x is as shown below.
In this question, we need to graph an equation y = 1/2 x on the coordinate plane.
First we find the the coordinates of points passing through y = 1/2 x
The function is undefined at x =0 .
For x = 1,
y = 1/2
For x = -1
y = -1/2
For x = 2,
y = 1/4
So, we get coordinates (1, 1/2), (-1, -1/2), (2, 1/4)
We plot these points on the coordinate plane.
Therefore, the graph of y = 1/2x is as shown below.
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