The expression that represents the combined function of f(x) and g(x) is h(x) = 2x/(5 - x)
How to determine the equation of the function h(x)?From the question, we have the following parameters:
Function f(x) = 2x
Function g(x) = 2 - x + 3
Evaluate the like terms in the equation of the function g(x)
So, we have
g(x) = 5 - x
From the question, we understand that:
The function h(x) is a combination of the functions f(x) and g(x) by division
This can be represented as
h(x) = f(x)/g(x)
The above also implies that the function h(x) is a composite function
Substitute the known values in the above equation
So, we have the equation of the composite function h(x) to be
h(x) = 2x/(5 - x)
Hence, the equation of the composite function h(x) is h(x) = 2x/(5 - x)
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the numbers between 1 to 2022 are written on a piece of paper.Caitlin circles the even numbers with red circles and nicole circles the multiples of 5 with yellow circles.How many numbers are circled with only one color?
The number of numbers circled with only one color found using arithmetic progression formula are 809 numbers
What is an arithmetic progression?An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms in the sequence is constant
The given parameters are;
The set of the numbers written on the paper = Numbers from 1 to 2022
Numbers circled with red circles by Caitlin = All even numbers between 1 and 2022
Numbers Nicole circles using yellow = Numbers that are multiples of 5
Required; The number of numbers that are circled with one colour only
Solution; The even numbers are numbers that are a multiple of 2
The number of even numbers between 1 and 2022 are found using arithmetic progression formula as follows;
[tex] a_{n} = a_{1} + (n - 1)\cdot d[/tex]
Where;
[tex]a_{1}[/tex] = The first term = 2 (First even number)
d = The common difference = 2
n = The number of terms
Given that 2022 is an even number, we have;
[tex] a_{n} = 2022 = 2 + (n - 1)\cdot 2[/tex]
Which gives;
[tex] \displaystyle {n = \frac{(2022 - 2)}{2} + 1 = 1011} [/tex]
We note that 10 is the lowest common multiple of 2 and 5, which gives;
Multiples of 10 have two colors, therefore, the numbers that have only one color is given by the difference between the number of even numbers and the number of multiples of 10 as follows;
The number of multiples of 10 are;
[tex] \displaystyle {n = \frac{(2020 - 10)}{10} + 1 = 202} [/tex]
Which gives;
The numbers having only one colour = 1011 - 202 = 809
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Jane, Alan, and Ravi sent a total of 146 text messages over their cell phones during the weekend. Ravi sent 8 fewer
messages than Jane. Alan sent 4 times as many messages as Ravi. How many messages did they each send?
Jane, Alan, and Ravi sent a total of 146 text messages over their cell phones during weekend, Ravi sent 8 fewer messages than Jane. Alan sent 4 times as many messages as Ravi. So as per question data,
Jane sent= 31 messages
Ravi sent= x-8= 31-8 = 23 messages
Alan sent= 4(x-8) = 92 messages
What operations are used here?The best way to solve an expression is from left to right if all the operations are the same (for instance, only addition, only subtraction, only multiplication, or only division). However, we must adhere to the order of operations for expressions including several operations.
The rule that dictates how to solve an expression involving numerous operations is known as the order of operations.
PEMDAS can help you remember that sequence. In PEMDAS, each letter denotes a mathematical operation.
Let, Jane sent x number of messages
Then, Ravi sent x-8 number of messages
and, Alan sent 4(x-8) number of messages
Total number of messages by them = 146
now,
x+(x-8)+4(x-8)=146
6x-40=146
x=31
so, Jane sent= 31 messages
Ravi sent= x-8= 31-8 = 23
Alan sent= 4(x-8) = 92
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Solve 7|14i-10|+9 = 37
Answer:
i = 1, (3/7)
Step-by-step explanation:
7|14i-10|+9 = 37,
-9 -9
------------------------
7|14i - 10| = 28
÷7 ÷7
---------------------
|14i - 10| = 4
14i - 10 = 4
+10 +10
------------------
14i = 14
÷14 ÷14
--------------
i = 1
|14i - 10| = -4
14i - 10 = -4
+10 +10
---------------------
14i = 6
÷14 ÷14
--------------
i = (3/7)
I hope this helps!
I really need to know how to solve for this question!! I have no idea what to do
Given:
Cost of Truck = $16000
Down payment amount = $3000
EMI = $250
Duration of EMI = 60 Months
Required:
a) Total amount financed
b) Total finance charge paid at the end of 60 months
Explanation:
Total cost of Truck = $16000
The total amount taken from other source = Total Amount - Down payment
=$16000-$3000
=$13000
EMI = $ 250
[tex]Total\text{ }amount\text{ }paid\text{ }at\text{ }the\text{ }end\text{ }of\text{ }60\text{ }months=250\times60[/tex][tex]Total\text{ }amount\text{ }paid\text{ }at\text{ }the\text{ }end\text{ }of\text{ }60\text{ }months=15000[/tex]Total amount paid at the end of 60 months = $15000
The total amount financed = Actual price -Down payment
=$16,000- $3000
=$13000
a) Total amount financed =3$18000
The total finance charged = Actual price - amount paid monthly for 60 months.
=$16000-$15000
=$1000
b)The total finance charged =1$20
Answer
Hence the total amount finance is 13000 dollar.
The total finance charged is 1000 dollar.00
Please help I’ll mark you as brainliest if correct!!
Answer:
A. 463-139=324
B. 14,527-7609=6918
Step-by-step explanation:
there ya go! hope it helps you out some!
let me know if it is correct
I want to place an order of 253,625 books. How can I estimate the number to make sure it’s enough books
The estimate where the number of books is enough is 254,000
What is the estimation of a number?The estimation of numbers is the approximation of the said number.
This means that the estimation of a number is close to the said number, but it has a slight different value
How to estimate the number of books?The number of books is given as
Number of books = 253,625
From the question, we understand that:
You want to make sure that the number of books is enough
This means that we estimate the number of books to a number greater than 253,625
A good way to do this is to approximate to the nearest thousand
When the number is approximated to the nearest thousand, we have
Estimate = 254,000
Hence, the estimate is 254,000
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Find the x-and y-intercepts of the line:3x - 4y = 12A.x-int: (-4,0)y-int: (0,3)B. x-int: (4,0)y-int: (0, -3)C. x-int: (0,4)y-int:(-3,0)D. x-int: (0,-4)y-int: (3,0)
To find the x-intercept, simply but y=0 in the equation given and solve for x
That is;
3x - 4y = 12
3x - 4(0) = 12
3x = 12
Divide both-side of the equation by 3
x= 4
The x-intercept is;
(4, 0)
To find the y-intercept, simply put y=0 in the equation given and then solve for y
That is;
3x - 4y = 12
3(0) - 4y = 12
-4y = 12
Divide both-side of the equation by -4
y = -3
The y-intercept is (0, -3)
Hence, the correct option is B.
x-int: (4,0)
y-int: (0, -3)
What is the value of x in the equation x^2 + 2 = 0
Answer:
[tex]{ \tt{ {x}^{2} + 2 = 0 }} \\ \\ { \tt{ {x}^{2} = - 2 }} \\ \\ { \tt{x = \sqrt{ - 2} }}[/tex]
- At this point, we can't operate the square root. Let's introduce the imaginary part of a value
From complex numbers;
[tex]{ \boxed{ \tt{{ \red{note} \: {\rightarrow{i \times i = - 1 = {i}^{2} }}}}}}[/tex]
Therefore;
[tex]{ \tt{x = \sqrt{2 \times {i}^{2} } }} \\ \\ { \boxed{ \rm{ \: x = i \sqrt{2} \: \: }}}[/tex]
write the sum in sigma notation [tex]\frac{1}{3} +\frac{1}{15} +\frac{1}{35} +\frac{1}{63}[/tex]
Sum in the sigma notation of the given series is equal to
∑[1 /(2n +1)(2n + 3)] , n =0,1,2,3.
As given in the question,
Given series :
(1 /3) + ( 1/ 15) + ( 1/ 35) + ( 1/ 63)
Simplify the given series
= [1/ (1 ×3)] + [1/ (3 ×5)] + [1/ (5 ×7)] + [1/ (7×9)]
1, 3, 5, 7 can be expressed as ( 2n + 1) , where n = 0, 1, 2, 3
3, 5, 7, 9 can be expressed as ( 2n + 3) , where n = 0, 1, 2, 3
Express the given series as a sum in the sigma notation form
(1 /3) + ( 1/ 15) + ( 1/ 35) + ( 1/ 63)
=∑ [ 1/ (2n +1) (2n + 3) ] where n = 0,1,2,3
Therefore, sum in the sigma notation of the given series is equal to
∑[1 /(2n +1)(2n + 3)] , n =0,1,2,3.
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Look at the diagram below that shows angle CAB ~ angle CED.
Which statement is TRUE?
A) D= 78 & E= 78
B) DCE= 24 & E= 77
C) D= 79 & E= 77
D) D= 77 & E= 79
The following statement is true about the triangles (d) D = 77 and E = 79
What is dilation?Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor,
Where the scale factor does not equal to one.
How to determine the true statements in the figure?From the attached image, we understand that there are two shapes
The shapes are triangles
One triangle is the scaled factor of the other
So, the triangles are similar shapes
As a general rule, the following are the properties of a scaled copy of another figure
If the scale factor is greater than 1, the side lengths would be greater than the original figureIf the scale factor is less than 1, the side lengths would be less than the original figureThe corresponding angles of both figures are the sameUsing the above as a guide, we have the following
D =B = 77 -- by corresponding angles
Also, we have
E = A = 180 - 77 - 24 -- by corresponding angles
E = A = 79
Hence, the true statement is (d) D = 77 and E = 79
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3) Recall problem 48 from your notes: Half an hour after leaving her house, Leah was 25 miles from
home. Leah then merged onto the freeway, and was able to travel at a constant speed for the next
several hours. Four hours after leaving her house, she was 280 miles from home.
a.
Find the model, m(t) that gives Leah's distance from home d in terms of the number of hours
she has been on the freeway, t.
b.
Suppose that Rachel lives 5 miles away from the same freeway entrance that Leah took. Rachel
leaves her house, and 10 minutes later is on the freeway. After 3.7 hours, Rachel is also 280 miles
away from her home.
i. What is Rachel's average speed on the freeway?
ii. Suppose that Rachel travels at a constant speed once she gets on the freeway. Write a
function k = f(t) that describes the number of miles she is from home, k, in terms of
the number of hours since she left home, t.
c. Assuming they are both traveling at a constant rate, who is driving faster? Give two different
answers to how you can see this
i. intuitively from the information provided.
ii. Algebraically from how you defined the functions.
Answer:
What is the role of ethnocentrism in defining the concept of “progress”
Step-by-step explanation:
Use the long division method to find the result when 8x^3-18x^2+24x+3 is divided by 4x-1. If there is a remainder, express the result in the form q(x)+r(x)/b(x).
Answer:
2x^2 -4x +5 +8/(4x -1)
Step-by-step explanation:
You want to divide 8x^3-18x^2+24x+3 by 4x-1 using polynomial long division.
Polynomial long divisionPolynomial long division is similar to numerical long division, except that the quotient term is always the ratio of the leading dividend term to the leading divisor term.
As with numerical long division, the dividend at each step is reduced by the product of the quotient term and the divisor.
When the dividend is of lower degree than the divisor, the division is finished. That dividend is the remainder.
The attachment shows the division in detail. Your result is ...
q(x) +r(x)/b(x) = (2x^2-4x+5) +(8)/(4x-1)
Construct a box-and-whisker plot for the given data.
The test scores of 40 students are listed below.
25 35 43 44 47 48 54 55 56 57
59 62 63 65 66 68 69 69 71 72
72 73 74 76 77 77 78 79 80 81
81 82 83 85 89 92 93 94 97 98
By median , test scores of 40 students are listed below. So five number summary is 25, 58,72,81,98
What are median in math?
The middle number is obtained by sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers). Example: Because the number 4 is in the middle when the numbers are ordered (1, 4, 7), it is the median of 4, 1, and 7.First we need to sort the data from Smallest to largest data value which is allready sorted
n = 40
Five number summary can be calculated as
Minimum = 25
Q1 can be calculated as
Lower Half of 40 values is 20, so median of 20 values will give us 25th percentile so Median = (20+1)/2 = 10.5th here 10th value is 57 and 11th value is 59 so Q1 = (57+59)/2 = 58
Median = (n+1)/2 = (40+1)/2 = 20.5th value and 20th and 21st value is 72 so median = (72+72)/2 = 72
Upper 20 values after median will provide us Q3 or 75th percentile which can be calculated as 20+(20+1)/2 = 30.5th value so 30th value is 81 and 31st value is also 81. So Q3 = (81+81)/2 = 81
Max = 98
So five number summary is 25, 58,72,81,98
And correct boxplot for this data is A. Boxplot A is correct which shows correct five number summary.
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The calculation for y=0y=0 corresponds to the
point where the graph crosses the________-axis. This is the point (______)
The calculation for y=0 corresponds to the point where the graph crosses the x-axis . This is the point (x,0) .
In the question ,
it is given that y=0 ,
When y=0 in a point (x,y) means , that point lies on the x -axis , and it is called as the x intercept .
X intercept is defined as the point where the graph of a line crosses the x-axis .
the point on the x-axis will be (x,0) ,
So , the graph will cross the x-axis when y=0 , and that point will be (x,0).
and the value of x will be called as the x intercept of the graph .
Therefore , the calculation for y=0 corresponds to the point where the graph crosses the x-axis . This is the point (x,0) .
The given question is incomplete , the complete question is
The calculation for y=0 corresponds to the point where the graph crosses the________-axis. This is the point (______) .
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x + 9.27 = 21
I need help answer this questions
Answer:
x = 11.73 is what i got
Step-by-step explanation:
Answer this question find angle a,b,c,d,e,f
We can determine the values of the angles as follows:
*By opposite by angle we will have that angle f is equal to:
[tex]f=180-44-78\Rightarrow f=58[/tex]angle f has a measurement of 58°.
*By supplementary angles we will have that angle e is equal to:
[tex]e=90-64\Rightarrow e=26[/tex]angle e has a measurement of 26°.
*As is indicated (Two lines have the same markings indicating they are parallel) we will have that the measurement of angle b is 78°.
*By complementary angles, the measurement of angle a is:
[tex]a=180-78\Rightarrow a=102[/tex]angle a has a measurement of 102°.
*We will have by alternate exterior angles that c has a measurement of 58°.
*By supplementary angles, we will have that the measurement of angle d equals:
[tex]d=180-58\Rightarrow d=122[/tex]angle d has a measurement of 122°.
Provide the correct reason for the statement in line 3. (please help)
Answer:
c) subtraction property of =
Step-by-step explanation:
step 3 show the movement of +15 moving to the other side of the = by subtracting 15 on each side, leaving you with 3x-16
Study Island Math Help Worth 40 PTS
Answer:
B
Step-by-step explanation:
using the rules of exponents
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
• [tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
given
[tex]5^{8}[/tex] × [tex](5^{12}) ^{-4}[/tex]
= [tex]5^{8}[/tex] × [tex]5^{(12(-4))}[/tex]
= [tex]5^{8}[/tex] × [tex]5^{-48}[/tex]
= [tex]5^{(8-48)}[/tex]
= [tex]5^{-40}[/tex]
= [tex]\frac{1}{5^{40} }[/tex]
Use the definition of a derivative to determine whether f(x) = 8x^2 is differentiable at x=0
The definition is option B No, it is not differentiable at x = 0.
Given,
The function, f(x) = 8x²
We have to find that the function is differentiable at x = 0.
So, lets check:
f(x) = 8x²
x = 0
f'(0) = [tex]\lim_{h\to \ 0}[/tex] [tex]\frac{f(0+h)-f(0)}{h}[/tex]
f(0 + h) = 8(0 + h)² = 8 (0 + 0 + h²) = 8h²
f(0) = 8 × 0² = 0
f(0 + h) - f(0) = 8h² - 0 = 8h²
f'(0) = [tex]\lim_{h \to \ 0}[/tex] 8h²/h = 8h = 8 × 0 = 0
That is, the function f(x) = 8x² is not differentiable at x = 0
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180
94
112
90
68
56
100
(x+18)° is vertical opposite 112° and vertical opposite angles are equal meaning
⇒(x+18)°=112°
x+18°=112°
x=112°-18°
∴x=94°
(2y)° is in a straight line with 112° meaning their sum is 180°
[tex]2y+112=180\\2y=180-112\\2y=68\\\frac{2y}{2} =\frac{68}{2} \\y=34[/tex]
∴y=34°
I need help with this this is my homework online
Given the exponential model
[tex]y=125000(0.95)^x[/tex]We can find the solution to the given question below.
hEe model says that between the year 2000 and 2001 the population of the boars decreased by 5%. The year 2000 indicates the starting point of the model.
[tex]\begin{gathered} Therfore,x=0 \\ y=125000(0.95)^0 \\ y=125000 \end{gathered}[/tex]Answer: 125000
Find the first three terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.an = 3n − 8
Solution:
To find the first three terms of the sequence defined as
This implies that we solve for
[tex]a_n[/tex]for n equals 1, 2, and 3.
Thus,
first term: n=1
[tex]\begin{gathered} a_1=3(1)-8 \\ \Rightarrow a_1=-5 \end{gathered}[/tex]second term: n =2
[tex]\begin{gathered} a_2=3(2)-8 \\ \Rightarrow a_2=-2 \end{gathered}[/tex]third term: n = 3
[tex]\begin{gathered} a_3=3(3)-8 \\ \Rightarrow a_3=1 \end{gathered}[/tex]Hence, the first three terms of the sequence are
[tex]-5,\text{ -2, 1}[/tex]Need help thanks. Due today
Answer:
The answer would be D(x/y)= -(11/8) / -(11/4)
Step-by-step explanation:
Given the initial inequality 2 > -4, identify whether the operation preserves the inequality symbol or reverses the inequalitysymbol.Add -2 to both sides.
ANSWER:
Preserves the inequality
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]2>-4[/tex]We add -2 on both sides and we have
[tex]\begin{gathered} 2-2>-4-2 \\ 0>-6 \end{gathered}[/tex]This is true, therefore the equality symbol remains the same
6-Mr. Lofters has 7/8 of a gallon of blue paint. He needs to distribute the blue paint out equally to his students. If Mr. Lofters pours 1/16 of a gallon of blue paint into each cup, how many cups of blue paint can he get? IMAGINE WHAT IS HAPPENING IN THE PROBLEM. WHAT OPERATION WILL BE INVOLVED? WHICH NUMBER WILL GO FIRST? LOOK FOR KEYWORDS. DO YOU REMEMBER THE FISH SONG?? YOU'LL REALLY FLIP IF YOU DON'T GET THIS ONE RIGHT.
We need to distribute 7/8 of a gallon into cups of 1/16 of a gallon. It means that to know the number of cups, we need to divide 7/8 into 1/16.
So, let's remember how to make a division between two fractions:
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}[/tex]Then, the division of 7/8 into 1/16 is equal to:
[tex]\frac{\frac{7}{8}}{\frac{1}{16}}=\frac{7\cdot16}{8\cdot1}=\frac{112}{8}=14[/tex]Therefore, he gets 14 cups of blue paint.
Answer: 14 cups
A pet store has 3 bird cages with 2 birds in each cage, and 10 aquariums with 4 fish in each aquarium. Which of the following expressions represents how many birds and fish the pet store owns?
(3+2)+(10 + 4)
(3+2) x (10+4)
(3 x 2) × (10 x 4)
(3 x 2) + (10 x 4)
Answer:
(3 × 2) + (10 × 4) is the correct expression.
what is the period of the graph of y=5sin(4piex)+3
The period of the graph is π/2.
What is the period of the graph?The length of one function wave is referred to as the period. One entire wave in this situation is 180 degrees, or radians. Without using a graph, you can get this simply dividing 2 by the frequency, which in this case is 2.
Given: 5 sin (4πx)+3
Period = 2π / 4
⇒ period = π/2
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Help PLEASE!!! How do I solve this?
Two similar boxes A and B are given with box B created by dividing box A's dimensions by 2.
Recall that the scale factor, k is the ratio of lengths of two corresponding sides of similar figures.
Since the dimensions of A were divided by 2 to form B, it follows that the scale factor of box A to box B is:
[tex]k=\frac{2}{1}[/tex]Also, recall the Similar Solids Theorem
It follows that the ratio of the volumes of the given solids is:
[tex]\frac{\text{Volume of A}}{\text{Volume of B }}=k^3=(\frac{2}{1})^3=\frac{2^3}{1^3}=\frac{8}{1}[/tex]Let the volume of box A be V₁ and let the volume of box B be V₂, it, therefore, implies that:
[tex]\frac{V_1}{V_2}=\frac{8}{1}[/tex]Substitute the value for the volume of box A into the equation, V₁=64:
[tex]\begin{gathered} \frac{64}{V_2}=\frac{8}{1} \\ Cross-Multiply_{} \\ \Rightarrow8V_2=64 \\ Divide\text{ both sides by 8:} \\ \Rightarrow\frac{8V_2}{8}=\frac{64}{8}\Rightarrow V_2=8\text{ cubic meters} \end{gathered}[/tex]Hence, the volume of box B is 8 m³.
A package of 5 pairs of insulated gloves costs $28.955. What is the unit price of the pairs of gloves ?
If a package of 5 pairs of insulated gloves costs $28.955,then the unit price of the pairs of gloves is $5.791
A package of 5 pairs of insulated gloves costs $28.955
The price of 5 pairs of insulated gloves = $28.955
Here we have to use the unitary method
The price of 1 pair of insulated gloves = The price of 5 pairs of insulated gloves / 5
Substitute the values in the equation and divide it
The price of 1 pair of insulated gloves = 28.955/5
= $5.791
Hence, if a package of 5 pairs of insulated gloves costs $28.955,then the unit price of the pairs of gloves is $5.791
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Jessica bought 3/5 of a pound of organic raspberries for $9 what is the cost of 1 1/3 pounds of raspberries
Using simple multiplication, the cost of 1 1/3 pounds of raspberries equals 12 pounds.
What is multiplication?Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.
Given,
Cost of 3/5 pounds of raspberries = $9
Cost of 1 pound of raspberries = 9 × 5/3
Cost of 1 pound of raspberries = 15 pounds
Cost of 1 1/3 pounds of raspberries = 4/3 × 15
= 12 pounds
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