Answer: The required expression is [tex]3x^3+2x^2+3x+2.[/tex]
Step-by-step explanation: We are given the following two functions :
[tex]f(x)=3x+2\\\\g(x)=x^2+1.[/tex]
We are to find the expression equivalent to [tex](f*g)(x).[/tex]
We know that
for any two functions p(x) and q(x), we have
[tex](p*q)(x)=p(x)\times q(x).[/tex]
Therefore, we get
[tex](f*g)(x)\\\\=f(x)\times g(x)\\\\=(3x+2)(x^2+1)\\\\=x^2(3x+2)+1(3x+2)\\\\=3x^3+2x^2+3x+2.[/tex]
Thus, the required expression is [tex]3x^3+2x^2+3x+2.[/tex]
Which would hold more water a teaspoon or a milliliter?
A particle's position is r⃗ =(ct2−2dt3)i^+(2ct2−dt3)j^,
where c and d are positive constants. Find expressions for times t > 0 when the particle is moving in the x-direction.
Solve x(−2) 2 =4(−2)
x(−2) 2 =4(−2) = -2
Explanation:To solve this equation, we first need to understand the order of operations in mathematical equations. The acronym PEMDAS is often used to remember the order: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
In this equation, we have parentheses and exponents. According to PEMDAS, we need to solve the parentheses first before moving on to the exponent. So, let's start by simplifying the parentheses on the left side of the equation.
x(-2)^2 = 4(-2)
= x(4) = -8
= 4x = -8
= x = -2
In the first step, we distributed the exponent of 2 to the -2 within the parentheses, resulting in (-2)^2 = (-2)(-2) = 4. This simplifies the left side of the equation to x(4) = 4x.
In the second step, we substituted the value of -2 on the left side of the equation, resulting in 4(-2) = 4x. This simplifies to -8 = 4x.
To isolate x, we divide both sides by 4, resulting in x = -2. This gives us our final answer.
In conclusion, when solving equations with multiple operations, it is important to remember the order of operations and follow it step by step. In this equation, we simplified the parentheses first, then solved for x by isolating it on one side of the equation. By following these steps, we were able to find the value of x, which is -2.
In November 2010, ING Direct was offering 2.4% interest on its Orange Savings Account, with interest reinvested quarterly.† Find the associated exponential model for the value of a $3,000 deposit after t years
What is the area of a circle with radius 14 units, to the nearest hundredth?
Find the angle measure of the hands of a clock at the given time. 5:00
The angle measured by the hands of a clock at the given time at 5:00 will be 150°.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
We know that the hour hand will be on 5 and the minute hand will be on 12 at 5:00 o'clock.
Then the angle measured by the hands of a clock at the given time at 5:00 will be
⇒ (360° / 12) x 5
⇒ 30° x 5
⇒ 150°
The angle measured by the hands of a clock at the given time at 5:00 will be 150°.
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A segment with endpoint M Left parenthesis 5 comma 9 right parenthesis and N Left parenthesis 4 comma 3 right parenthesis is rotated 270°. What are the coordinates of M prime and N prime?
The correct answer is : M prime (9,-5) and N prime (3,-4)
There are 3 in. of snow on the ground when it begins to snow 0.5 in. /h.
Which linear equation represents the total depth of the snow, in inches, after x hours?
A. y=0.5x
B. 3+y=0.5x
C. y=0.5x+3
D. x=0.5y
Answer:
c. i took the test
Step-by-step explanation:
The required linear equation y = 0.5x + 3 represents the total depth of the snow, in inches, after x hours which is the correct answer would be option (C).
What exactly is a linear equation?A linear equation is one in which the greatest power of the variable is always one.
The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
We have been given that there is 3 in. of snow on the ground when it begins to snow 0.5 in. /h.
Let the total depth of the snow, in inches, after x hours
As per the given information, translate the phrase into an algebraic form:
y = 0.5x + 3
Here y represents the total depth of the snow.
Therefore, the correct answer would be option (C).
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Evaluate these questions
3a+2a=
c+d there is a line under this one
ad
Look at the diagram. If RS= 8y + 4, ST = 4y + 8, and RT = 36, find the value of y.
Answer:
(A) y=2
Step-by-step explanation:
It is given that [tex]RS=8y+4[/tex], [tex]ST=4y+8[/tex]and [tex]RT = 36,[/tex] then
According to the figure given, we have
[tex]RT=RS+ST[/tex]
[tex]36=8y+4+4y+8[/tex]
[tex]36=12y+12[/tex]
[tex]24=12y[/tex]
[tex]y=\frac{24}{12}[/tex]
[tex]y=2[/tex]
Thus, the value of y will be 2.
Hence, option A is correct.
Mikel creates the table below to help her determine 40% of 70
To Find: 40 % of 70
Solution:
x % of y means = [tex]\frac{x \times y}{100}[/tex]
40 % of 70= [tex]\frac{40 \times 70}{100}=\frac{2800}{100}=28[/tex]
This is the way Mikel can determine 40 % of 70.
Algebra problem below!
The sum of two consecutive even integers is -50
What are the numbers?
Jeff wants to make an a in his math course this semester. To do so, he must have an average of 90 or above. If his test scores this semester or 88, 92 and 96 what is the score that he would need to make on his final test to attain an average on exactly 90
if a right triangle has side lengths x + 9, x + 2, x + 10 is the hypotenuse, find the value of x
To determine the value of x for the right triangle, we applied the Pythagorean theorem to the side lengths and solved the resulting quadratic equation, revealing x to be -1.
Explanation:To find the value of x for the side lengths of a right triangle with side lengths x + 9, x + 2, and x + 10 as the hypotenuse, we use the Pythagorean theorem, which states that in a right triangle, a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the two other sides.
Here's the step by step solution:
Write the Pythagorean theorem with the given side lengths: (x + 2)² + (x + 9)² = (x + 10)².Expand the squares: x² + 4x + 4 + x² + 18x + 81 = x² + 20x + 100.Combine like terms and move all terms to one side: x² + 22x + 85 = 0.Solve the quadratic equation, which yields x = -1 or x = -85. However, since side lengths cannot be negative, the only logical value of x is -1.
Final answer:
To find the value of x in a right triangle with sides x + 9, x + 2, and hypotenuse x + 10, the Pythagorean theorem is used. After applying the theorem, we simplify and solve the resulting quadratic equation, which gives us a positive value of x = 3.
Explanation:
The student is asking how to find the value of x in a right triangle with sides x + 9, x + 2, and x + 10, where x + 10 is the hypotenuse. To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².
For this particular triangle:
Identify the legs and the hypotenuse of the triangle: Leg 1 is x + 9, Leg 2 is x + 2, and the Hypotenuse is x + 10.Apply the Pythagorean theorem: (x + 9)² + (x + 2)² = (x + 10)².Simplify and solve for x. Expand the squares: x² + 18x + 81 + x² + 4x + 4 = x² + 20x + 100.Combine like terms and move all terms to one side of the equation:(2x² + 22x + 85) - (x² + 20x + 100) = 0x² + 2x - 15 = 0Factor the quadratic equation: (x + 5)(x - 3) = 0Find the possible values for x: x = -5 or x = 3. Since a side length can't be negative, the value for x must be 3.Therefore, the value of x is 3.
Parallelogram JKLM is shown on the coordinate plane below:
If parallelogram JKLM is rotated 270° clockwise around the origin, what are the coordinates of the endpoints of the side congruent to side JM in the image parallelogram?
Answer-
The coordinates of the endpoints of the side congruent to side JM will be,
(-2, -6) and (1, -5).
Solution-
When rotating a point 270° clockwise or 90° counter-clockwise around the origin, we apply the rule (x, y) → (-y, x).
The co-ordinates of the original parallelogram are,
J = (-6, 2)
M = (-5, -1)
L = (-3, 3)
K = (-4, 6)
After the rotation, the new co-ordinates will be,
J = (-2, -6)
M = (1, -5)
L = (-3, -3)
K = (-6, 4)
∴ The coordinates of the endpoints of the side congruent to side JM will be,
(-2, -6) and (1, -5).
The distributive property is used to help simplify math experssions. True False
Hey!
Hope this helps...
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
TRUE
This is because when you distribute 1 thing between 2 (or more) things, it (in a way) simplifies the problem...
For Example:
solve for x
f(x) = 5*(x - 4)
The only way to solve a question like this would be to distribute the 5 to the x and to the 4...
So...
The answer is: TRUE
Can someone help me with 11? I’m confused on how to solve for the rest of the problem. I don’t know how to get rid of the 3
Points a, b, c, and d are collinear. in how many ways can the line be named using only these points
Staci has seven more cats then Taylor. Write an expression that illustrates how many cats Staci has. Use x to represent the number of cats Taylor has./4899345/032a37eb?utm_source=registration
Write a story that matches the expression
42x - 5
Answer: Hello there!
The equation is: 42x - 5
That can be phrased as "the difference between 42 times a number x and 5"
And we want to write a story that matches this.
an example can be:
Suppose that Jon craft musical instruments and he sells them in the beach, then you could write:
"The revenue in a day for Jon is equal to $42 for each instrument that he sells, less a 5 dollar fee that he needs to pay every day"
where the number of instruments would be x.
Suppose that (y) varies with (x). Write an equation for the inverse variation.
y=4 when x=7
A: y= x/28
B: y=3x
C: x= y/3
D: y= 28/x
y = k/x, where k is the constant
if x = 7 and y = 4
4=k/7
k = 4*7 = 28
y = 28/x
answer is D
One month, Ruby worked 8 hours more than Isaac, and Svetlana worked 4 times as many hours as Ruby. Together they worked 112 hours. Find the number of hours each person worked.
1. Find the perimeter and area of a rectangle with a length of 3.2 m and a width of 1.5 m.
A) p=4.7 m; A=2.25 m^2
B) p=4.7 m; A=4.8^2
C) p=9.4 m; A=2.4 m^2
D) p=9.4 m; A= 4.8^2
2. Find the area of a triangle with a base of 27 feet and a height of 14 feet.
A) 41 ft^2
B) 82 ft^2
C) 189 ft^2
D) 378 ft^2
The line segments are translated 2 units to the left to form J′K′ and M′N′. Which statement describes J′K′ and M′N′?
Answer:
Step-by-step explanation:
the line segments J'K' and M'N' do not intersect and are the same distance apart as JK and MN.
What is the common term for the set of all points with x- coordinate zero?
A. X axis
B. Y axis
C. Coordinate plane
D. Origin
Can u solve 6x-21=5x+17+x
Point M is the midpoint of segment JK. Find JK when JM=6x-7 and MK=2x+3.
The value of JK will be 16.
It is given that M is the midpoint of segment JK.
We have to find out the value of JK.
What will be the value of x , if 4x + 12 = 8x + 4 ?
The value of x will be 2.
As M is the midpoint of JK.
JK = MK + JM
So,
MK = JM
2x + 3 = 6x - 7
4x = 10
x =2.5
So ,
MK = 2x + 3 = 8
JM = 6x - 7 = 8
Hence ,
JK = MK + JM = 8 + 8
JK = 16
Thus , value of JK will be 16.
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Five times a number is equal to the number increased by 12
The required expression is [tex]5n = n+ 12[/tex] and the unknown number is [tex]3[/tex]
Let the unknown number be "n"
Five times the number is expressed as 5nThe number increased by 12 is expressed as n + 12Equating both expressions will give:
[tex]5n = n + 12[/tex]
Solve for n:
[tex]5n - n = 12\\4n = 12\\n = 12/4\\n = 3[/tex]
Hence the required expression is [tex]5n = n+ 12[/tex] and the unknown number is [tex]3[/tex]
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what do you add 15/4 to make 4
luke scored 21 goals in 7 soccer games. if he scores goals at the same rate, how many goals will he score in 23 games
Answer:
69
Step-by-step explanation:
My bad if it's wrong