Mathematics High School
Answers
Answer 1
The answer of the given function is [tex](fg)(x) = 2x^3+7x^27x3[/tex]. So the answer is C option.
What does f(x) mean?
f(x) is a function that can be named to avoid repeatedly writing it out. The function's name is f, and we are providing the variable x to it.
And g(x) also has a similar meaning.
The given question is a quadratic equation problem.
Given: f(x)= 2x³+7x²4x5
And g(x)= 3x2
To find: (fg)(x) we have to simply subtract the above to equations
That is [tex](fg)(x)[/tex] = 2x³+7x²4x5(3x2)
On opening the brackets we get;
[tex](fg)(x)[/tex]= [tex]2x^3+7x^24x53x+2[/tex]
[tex]= 2x^3+7x^2 7x  3[/tex] { here we subtracted and added the like terms together}.
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Related Questions
Rachel is making premade 3inch by 5inch tile rectangles for her driveway. If it takes her 6 minutes to position each rectangle, how many hours will it take her to create a 2foot by 4foot pattern drive? Write your answer as a decimal.
Answers
This is a Metric conversion problem. Note that it will take 38.4 minutes to create a 2foot by 4foot pattern drive. See the explanation below.
What is the calculation justifying the above answer?
There are several ways to do this. Let's use the area of the times and that of the pattern drive.
Note that the area of the 3inch by 5inch tile =
Area of a rectangle
L x B =
3 x 5
= 15inches
Applying the same rule to the pattern drive, we have
2 x 4
= 8 foot
Note that 1 foot = 12 inches
For convenience, thus, we convert the area of the pattern drives into inches. This gives us:
8 x 12
= 96 inches
To get how many minutes it will take to create a 2 by 4foot pattern drive, we have
Recall that it takes 6 minutes to lay a 3x5 which is 12 inches in area.
Hence,
96/15
= 6.4
6.4 x 6
= 38.4 minutes.
Hence, it will take Rachel 38.4 minutes to lay a 2 by 4foot pattern drive given the parameters above.
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rewrite 5+3/4x=3/8 so it doesn't have fractions
Answers
Answer:
40 + 6x = 3
Stepbystep explanation:
Multiple all the way through by 8
8( 5 + [tex]\frac{3}{4}[/tex] x) = ([tex]\frac{3}{8}[/tex])8
8(5) + [tex]\frac{8}{1}[/tex][tex](\frac{3}{4})[/tex]x = [tex]\frac{3}{8}[/tex][tex](\frac{8}{1})[/tex]
40 + 6x = 3
Simplify.
3c + 6d + 3d
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{3c + 6d + 3d}\\\large\text{COMBINE the LIKE TERMS}\\\mathsf{= (3c) + (6d + 3d)}\\\mathsf{= 3c + 6d + 3d}\\\mathsf{= 3c + 9d}\\\huge\text{Therefore, your answer should be: \boxed{\mathsf{3c + 9d}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
What is the equation of the line that passes through the point (3,2) and has a slope of 2/3
Answers
Answer: y = 2/3 2
Stepbystep explanation: using a graph you can plot the point (3, 2).
After this, you can use the slope of 2/3 to graph the starting point. You go 3 to the left and 2 up going through the y axis of 2. using y = mx + b, you can plug in the slope of 2/3 and the starting point of 2.
let in the region where . explain why must have a global minimum at some point in (note that is unboundedhow does this influence your explanation?). then find the global minimum. minimu
Answers
the formula for a function of the form y= a е⁻ˣ +b x with global minimum at (1,10) is y= 5е¹ ⁻ ˣ +5 x
We can use first and second derivative tests to determine all coefficients of the function described in statement so that the point given is an absolute minimum. The expressions for such tests are introduced below:
First Derivative Test
a .е⁻ˣ +b = 0 (1)
b=a .е⁻ˣ
Second Derivative Test
y''= a . .е⁻ˣ (2)
Where y'' >0
If we know that ( x,y) = 9 1,10) , then we have the following system:
10 = a е⁻¹ +b (3)
b= a е⁻¹ (4)
y'' = a е⁻¹ (5)
By (4) in (3):
10= 2aе⁻¹
a=10/2е⁻¹
a= 5е
By (5) we prove that y''>0, and we get the value of by (4):
b=5
Thus, the formula for a function of the form y= a е⁻ˣ +b x with global minimum at (1,10) is . y= 5е¹ ⁻ ˣ +5 x
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what is 2/3 times 1/16
Answers
Answer:
1/24
Stepbystep explanation:
Answer:
1/24
Stepbystep explanation:
so first you cross out the 2 and 16 because 2*8=16
then you multiply the numerator and the denominator.
then bam! your answer!
1/24
suppose that you have 15 quarters, 10 dimes, 10 nickels, and 10 pennies in your pocket. you reach in and choose a coin at random so that you can give it to your child. what is the expectation? (round your answer to two decimal places.)
Answers
If you have 15 quarters, 10 dimes, 10 nickels and 10 pennies, then the probabilities of getting quarter, dimes, nickels and pennies are 0.33, 0.22, 0.22 and 0.22 respectively.
Total number of quarters = 15 quarters
Total number of dimes = 10 dimes
Total number of nickels = 10 nickels
Total number of pennies = 10 pennies
Total number of coins = 15+10+10+10 = 45
The probability of getting a quarters = 15/45
= 0.33
The probability of getting a dimes = 10/45
= 0.22
The probability of getting a nickel = 10/45
= 0.22
The probability of getting penny = 10/45
= 0.22
Hence, if you have 15 quarters, 10 dimes, 10 nickels and 10 pennies, then the probabilities of getting quarter, dimes, nickels and pennies are 0.33, 0.22, 0.22 and 0.22 respectively.
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I don’t know what I’m doing wrong for this
Answers
Answer:
Stepbystep explanation:
I guess you want to draw the graph.
The graph is a straight line
6x  20 = 4y
When x = 0:
6(0)  20 = 4y
y = 20/4 = 5
So, one point on the graph
= (0, 5)
When y = 2:
Plugging y = 2 into the equation:
6x  20 = 4(2)
6x = 8 + 20 = 12
x = 2
So, another point is (2, 2)
Mark these 2 points on the graph paper
and draw a line passing through them.
Sandeep is making fruit dip for a party. His recipe calls for 1/2 of a teaspoon of cinnamon and 3/4 of a cup
of yogurt. Using this ratio, how much cinnamon does Sandeep need if he uses 3 cups of yogurt?
Answers
2 teaspoon of cinnamon need if he uses 3 cups of yogurt
What is ratio ?
By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part to part ratio, whereas the second is a part to whole ratio. The relationship between two separate entities or organizations is shown by the parttopart ratio. For instance, a class has a 12:15 boytogirl ratio, whereas the parttowhole ratio describes how one group compares to another. For instance, five people enjoy reading books out of every ten persons. Since the ratio of the component to the total is 5:10, 5 out of every 10 persons enjoy reading.
Given that :Sandeep is making fruit dip for a party. His recipe calls for 1/2 of a teaspoon of cinnamon and 3/4 of a cup
of yogurt.
[tex]0.5 : 0.75 = x : 3[/tex]
x = 2
2 teaspoon of cinnamon need if he uses 3 cups of yogurt
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Estimate the quotient of 41 ÷ 7.94.
4
5
6
7
Answers
8x5 equals 40 so 5 should be your best estimate
The graph of the equation 2x3y=7 is a line. Find the x and yintercepts and graph the line using these two points.
Answers
xintercept, 7/2
yintercept, 7/3
What is intercept?
The points where a line crosses an axis are known as the xintercept and the yintercept, respectively. the location on the y axis where a graph crosses it. • x = 0 at the same location. An intercept in mathematics is a location on the yaxis through which the line's slope passes. It is a place on the yaxis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx+c, where m denotes slope and c denotes the yintercept.
Given that,
The graph of the equation 2x3y=7 is a line.
2x3y=7
Divide 7 on both sides
2x/7 3y/7=1
[tex]\frac{x}{7/2} \frac{y}{7/3} =1[/tex]
xintercept, 7/2
yintercept, 7/3
Therefore, xintercept, 7/2, yintercept, 7/3.
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the question is in the picture
Answers
Given
[tex]S=\mleft\lbrace1,2,3,4,5,6,7,8,9\mright\rbrace[/tex]
by selecting two numbers from S, the number of possible outcomes is
[tex]n(S)=9\times9=81[/tex]
Let E be the event that selecting two numbers randomly and their sum is 12 with replacement.
[tex]E=\lbrack(3,9),(4,8),(5,7),(6,6),(7,5),(8,4),(9,3)\}[/tex][tex]n(E)=7[/tex]
The probability is
[tex]P(E)=\frac{n(E)}{n(S)}[/tex]
Substitute values, we get
h is
[tex]P(E)=\frac{7}{81}[/tex]
b)without replacement
Areplacementout
[tex]A=\mleft\lbrace(3,9\mright),(4,8),(5,7),(7,5),(8,4),(9,3)\}[/tex][tex]n(A)=6[/tex]
[tex]P(A)=\frac{n(A)}{n(S)}[/tex]
Substitute the values, we get
[tex]P(A)=\frac{6}{81}=\frac{2}{27}[/tex]
The probability that the sum is 12 if selecting two numbers without replacement
[tex]P(A)=\frac{2}{27}[/tex]
500 divided by 2/3 = 500 x _ = _ feet
Answers
Answer:
500 divided by 2/3 = 500 * 3/2= 750
Stepbystep explanation:
Write a complete twocolumn proof for following information.
B
C
Given: AB = 3y  1, BC = 7y, AC = 29
Prove: AB = 8
Answers
Hence proved that triangle AB = 3(3)  1 = 9  1 = 8.
What is triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the display style for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a twodimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle. All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higherdimensional Euclidean spaces. Except when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.
Given that,
AB + AC = AC
3y  1 + 7y = 29
10y = 29 + 1 = 30
y = 30/10 = 3
Therefore, AB = 3(3)  1 = 9  1 = 8.
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This question is not from a test. This is an extra credit MATHS assignment. Please help me if you can. If you do, thank you! :)
Answers
we have the equation
[tex]y=31sin5x+32[/tex]
Find out the first derivative
[tex]\begin{gathered} y^{\prime}=(5)(31)c0s5x \\ y^{\prime}=155cos5x \end{gathered}[/tex]
equate to zero the derivative, to find out the critical points
[tex]\begin{gathered} 155cos5x=0 \\ cos5x=0 \end{gathered}[/tex]
The value of cosine is zero when the angle is 90, 270 degrees (pi/2 and 3pi/2)
so
[tex]\begin{gathered} 5x=\frac{\pi}{2} \\ \\ x=\frac{\pi}{10} \end{gathered}[/tex][tex]\begin{gathered} 5x=\frac{3\pi}{2} \\ \\ x=\frac{3\pi}{10} \end{gathered}[/tex]
For x=pi/10
Find out the ycoordinate
[tex]\begin{gathered} y=31s\imaginaryI n\frac{5\pi}{10}+32 \\ \\ y=31sin\frac{\pi}{2}+32 \\ \\ y=31+32=63\text{ ft} \end{gathered}[/tex]
Verify for x=3pi/10
[tex]\begin{gathered} y=31s\imaginaryI n5(\frac{3\pi}{10})+32 \\ \\ y=31s\imaginaryI n(\frac{3\pi}{2})+32 \\ y=31+32=1\text{ ft} \end{gathered}[/tex]The maximum height is 63 ft
Select all the equations where x = 2 is a solution.
(Select all that apply.)
a. 3x  5 = 1
b. 19 = 2(x6)+3
c. 5 + 3x = 1
d. 2(x+5)=x+8
e. 4x = 4 + 2x
Answers
the leters c and d are correct for this equation
What 685,203 rounded to the nearest ten , hundred , thousand, ten ten thousand and, hundred thousand
Answers
Answer:
685200 is ten and hundred 685000 thousand 690000 ten thousand 700000 hundred thousand
the question is the png
Answers
Answer:
this appears to already be in standard form?
Stepbystep explanation:
standard form has x and y on one side of the =
After 5 years, $8,000 deposited in a savings account with simple interest had earned $3,600 in interest. What was the interest rate?
Answers
Answer:
9%
Stepbystep explanation:
So first we need to find how much interest he got in a single year.
3600 ÷ 5 = 720
Now we find out how much 720 is compared to 8000.
720 ÷ 8000 = 0.09
Then we make that a percentage:
9%
When rolling 3 standard number cubes, the probability of getting all three numbers to match is 6/216. What is the probability that the three numbers do not all match?
If your answer is a repeating decimal, type the repeated portion of the decimal only once.
For example:
for you only type in 3.6
for you only type in 0.45
copied for free from openupresources.org
Answers
Is Tishri rifle with the guns that you have gun in the king or something in that bc of you a gun or not fake or a gun or something or just a cop or a mod or a gang owner or not fake or not even in a general area or a gun store in where you
Write the equation of the line that passes through points (2,0) and (3,4) in pointslope form.
Answers
Answer:
y0 = [tex]\frac{4}{5}[/tex](x +2)
or
y  4 = [tex]\frac{4}{5}[/tex](x 3)
These both mean the same thing.
Stepbystep explanation:
First, we have to find the slope. The slope is the change in y over the change in x.
Our y's are 4 and 0 and your x's are 3 and 2
[tex]\frac{40}{3  2}[/tex] = [tex]\frac{40}{3+2}[/tex] = [tex]\frac{4}{5}[/tex]
Now that we have the slope, we can use either point to write the eqation.
If we use point (2,0)
The equation is
y  [tex]y_{1}[/tex] == m(x [tex]x_{1}[/tex]
y  0 = [tex]\frac{4}{5}[/tex] (x  2)
y  0 = [tex]\frac{4}{5}[/tex](x +2)
If we use the point (3,4)
y4 = [tex]\frac{4}{5}[/tex](x 3)
Evaluate the expression if
m
=
−
4
,
n
=
1
,
p
=
2
,
q
=
−
6
,
r
=
5
,
and
t
=
−
2
.

16
+
4
(
3
q
+
p
)
Answers
The numeric value of the expression 16 + 4(3q + p) when q = 6 and p = 2 is given by: 96.
How to find the numeric value of a function or of an expression?
To find the numeric value of a function, we replace each instance of the variable in the function by the desired value. This also works for multivariable functions or expressions, as each instance of each variable will be replaced by their attributed values.
For this problem, the expression is given by:
16 + 4(3q + p)
The attributed values are given by:
q = 6, p = 2.
Hence the numeric value of the expression is found as follows:
16 + 4(3 x 6 + 2) = 16 + 4(18 + 2) = 16 + 4 x 20 = 16 + 80 = 96.
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Complete the twoway frequency table below, which shows the relationship between students who enroll in advanced algebra and physics in a particular high school. From a sample of 40 students, it is found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both. How many students are enrolled in either algebra or physics?
Algebra Not in Algebra Total
Physics 5 14
Not in Physics
Total 29 40
33
38
2
5
Answers
Answer:38
Stepbystep explanation:
sense it subteact between
Answer: 38
Stepbystep explanation: subtract between
lenge You buy 3.16 pounds of oranges, 1.15 pounds of peaches, and 2.24 pounds of apples.
Answers
Using the addition, if you buy 3.16 pounds or oranges, 1.15 pounds of peaches and 2.24 pounds of apples , then the total bill is 6.55 pounds
The cost of the oranges = 3.16 pounds
The cost of the peaches = 1.15 pounds
The cost of the apples = 2.24 pounds
Then the total bill = The cost of the oranges + The cost of the peaches + The cost of the apples
Here we have to use the addition
Substitute the values in the equation
Then the total bill = 3.16 + 1.15 + 2.24
= 6.55 pounds
Hence, using the addition, if you buy 3.16 pounds or oranges, 1.15 pounds of peaches and 2.24 pounds of apples , then the total bill is 6.55 pounds
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Find the domain of the graphed function.
OA. 9≤x≤ 5
OB. 0≤x≤ 10
OC. x20
10
D. x is all real numbers.
10
10
PLEASE HURRY
Answers
The domain of the graphed function is option (D)
What is the domain of a graphed function?
In mathematics, the domain of a function is the set of inputs that the function accepts. It is also known as dom(f) or dom f, where f is the function.
The domain of the graphed function is option (D) x is all real numbers.
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Write an algebraic expression to represent each statement
50 added to half of a number, c
Answers
The expression represented by 50 added to half of a number, c is 50 + c/2
What are expressions?
Expressions are mathematical statements that are represented by variables, coefficients and operators
How to translate the algebraic expression?
The expression is given as
50 added to half of a number, c
half of a number, c means divide c by 2
So, we have
50 added to half of a number, c => 50 added to c/2
Added to means +
So, we have
50 added to half of a number, c => 50 + c/2
Hence, the expression represented by the statement is 50 + c/2
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need help asap
do please asap
help
Answers
The diagram attached below shows the rectangles with the following:
a. Perimeter = 30 cm; b. Perimeter = 30 cm
c. Length = 8 cm; Width = 4 cm
Length = 10 cm; Width = 2 cm
Length = 7 cm; Width = 5 cm
What is the Perimeter of a Rectangle?
A rectangle is a four sided shape that has two opposite sides that are parallel and equal to each other.
The perimeter of a rectangle is the sum total of all the four sides of the rectangle and can be calculated using the formula:
Perimeter of a rectangle =2(length + width).
3. a. The diagram of the rectangle that has the following parameters is shown as rectangle 1 in the image attached below, where:
Length of rectangle = 10 cm
Width of rectangle = 5 cm
Perimeter of rectangle 1 = 2(10 + 5) = 30 cm
b. Rectangle 2 in the diagram shows the parameters given:
Length of rectangle = 20 cm
Width of rectangle = 10 cm
Perimeter of rectangle 2 = 2(20 + 10) = 60 cm
c. Rectangles 3, 4 and 5 shows the different measures a rectangle with a perimeter of 24 cm can be:
Rectangle 3: Length = 8 cm; Width = 4 cm
Rectangle 4: Length = 10 cm; Width = 2 cm
Rectangle 4: Length = 7 cm; Width = 5 cm
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The points (0,k) and (1,4) fall on a line with a slope of 9. What is the value of k?
Answers
Answer:
Formula for gradient is given as (y2y1)÷(x2x1) or (y1y2)÷(x1x2), where x and y are the coordinates of the points.
(k4)÷(01) = 9
k4 = 9(01)
k4 = 9
k = 5
#2 The number of bacteria in a refrigerated food is given by N(T)=20T220T+120 for 2T14 Tand where T is the temperature of the food in Celsius.
(a)Explain the meaning of 2T14 in this context
(b)Determine the temperature the number of bacteria will be minimal?
(c)Find number of bacteria in a above
(d) Sketch a graph
Answers
From the given quadratic function, it is found that:
a) The interval 2 ≤ T ≤ 14 gives the range of the temperature of the food in Celsius.
b) The number of bacteria will be minimal for a temperature of 0.5 ºC.
c) The minimum number of bacteria is of 115.
d) The graph that models the situation is sketched at the end of the answer.
What does the quadratic function models in this problem?
The quadratic function is given as follows:
N(T) = 20T²  20T + 120, 2 ≤ T ≤ 14.
In which:
T is the temperature in Celsius of the food.N(T) is the number of bacteria in the food.
The function has a domain of 2 ≤ T ≤ 14, meaning that these are the possible temperatures of the food.
For a concave up quadratic function, the minimum value happens when the input is of:
Tm = b/2a.
For this problem, the coefficients of the quadratic function are as follows:
b = 20, a = 20.
Hence the temperature in which the number of bacteria will be minimal is of:
Tm = 20/40 = 0.5 ºC.
The number of bacteria with this temperature is given by the numeric value of the function when T = 0.5, that is, each instance of T in the function is replaced by 0.5, hence:
N(0.5) = 20(0.5)²  20(0.5) + 120 = 115 bacteria.
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What are the domain and range of this relation? pt3 last one pls help
Answers
The range of a relation is the set of the second coordinates from the ordered pairs. This tutorial defines the range of a relation!