the fuction f(x) is equal to:
[tex]f(x)=-x+7[/tex]now, to evaluate f(15) we have to replace x=15 so the equation is going to be equal to:
[tex]f(15)=-15+7=-8[/tex]United States Postal Service handled 7.2 x 10¹0 mails in the year 1965. They handled 1.8 x 10¹¹ mails in
the year 1995. How many more pieces of mail were handled by the United States Postal Service in
1995 than in 1965?
4.0 x 10¹
4.0 x 1010
O 5.4 x 10¹0
O 1.08 x 10¹¹
The number of mail were handled by the United States Postal Service in 1995 than in 1965 is 0.4.
Given that, United States Postal Service handled [tex]7.2 \times 10^{10}[/tex] mails in the year 1965. They handled [tex]1.8 \times 10^{11}[/tex] mails in the year 1995.
What is scientific notation?Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as [tex]1.56\times10^7[/tex].
Number of mail were handled by the United States Postal Service in
1995 than in 1965 = Number of Postal Service handled mails in the year 1965 ÷ Number of Postal Service handled mails in the year 1995
= [tex]\frac{7.2 \times 10^{10}}{1.8 \times 10^{11}}[/tex]
= 4 × [tex]10^{-1}[/tex]
= 0.4
Therefore, the number of mail were handled by the United States Postal Service in 1995 than in 1965 is 0.4.
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U = {1,2,3,4,5,6,7,8,9,10} is the universal set, and P = {1,3,5,7,9}. What is P?
The sets of P is a subsets of the universal sets.
How to solve sets?Sets are defined as the collection of objects whose elements are fixed and can not be changed.
In other words, a set is a collection of elements or numbers or objects, represented within the curly brackets { }. For example a collections of alphabets {a, b, c, d, e, f, g, h}
Therefore, universal set (usually denoted by U) is a set which has elements of all the related sets, without any repetition of elements.
Hence,
universal set = ∪ = {1,2,3,4,5,6,7,8,9,10}
Therefore,
P = {1,3,5,7,9}.
P is a subsets of the universal sets.
The subsets is a part of the universal set.
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please show all work
Given:
[tex]f(x)=3\csc (x+6)-4[/tex]To find:
We need to find the same transformation of the given function.
Explanation:
[tex]\text{Let g(x)=3csc(x) be the parent function of the given function.}[/tex]The function g(x) is translated 6 units right and 4 units down to get f(x).
Consdier the function :
[tex]f(x)=3e^{x+6}-4[/tex][tex]\text{ Let g}\mleft(x\mright)=3e^x\text{ be the parent function.}[/tex]:
[tex]f(x)=3(x+6)^2-4[/tex][tex]\text{ Let g}\mleft(x\mright)=3x^2\text{ be the parent function.}[/tex]Final answer:
The following functions have the same transformation as give f(x0.
[tex]f(x)=3e^{x+6}-4[/tex][tex]f(x)=3(x+6)^2-4[/tex]On the axes below,sketch two full cycles of your chosen riders Ferris wheel. Adrianes Ferris wheel goes from 10 feet above the ground to a maximum height of 210 feet and completes one revolution every 90 seconds.
ANSWER
EXPLANATION
First, we have to draw horizontal lines at the minimum and maximum heights. These are 10 feet and 210 feet, respectively.
Then, we calculate the midline,
[tex]y_m=\frac{210ft+10ft}{2}=\frac{220ft}{2}=110ft[/tex]And we have to draw this line too.
As mentioned, the period is the time it takes to do one revolution, which this wheel makes in 90 seconds. Thus, the period is 90 seconds and the first cycle starts at t = 0 and ends at t = 90 s,
Then, we know that the graph is sinusoidal, so we have to draw the first cycle - note that if the period is 90 s, the graph must intersect the midline at 45 seconds,
And finally, draw another cycle just like the first one.
Find the real number solution(s) to the polynomial function f(x) = (x + 9)(x − 5)(x + 7).
a
x = −5, 7, 9
b
x = −9, −7, 5
c
x = −280
d
x = 11
For the given polynomial function f(x) =(x+9)(x-5)(x+7) the real number solutions are x = -9, -7,5.
As given in the question,
Given polynomial function :
f(x) =(x+9)(x-5)(x+7)
Real number solutions for the given polynomial function
f(x) =(x+9)(x-5)(x+7)
Values for which f(x) =0
0= (x+9)(x-5)(x+7)
Equate all the value to zero we get,
⇒ (x+9) =0 , (x-5) =0 , (x+7) =0
⇒ x = -9 , 5, -7
For x= -9 , 5, -7 polynomial function f(x) =(x+9)(x-5)(x+7) value is equal to zero.
Therefore, for the given polynomial function f(x) =(x+9)(x-5)(x+7) the real number solutions are x = -9, -7,5.
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Help me !!!!!!!!! I need this for today
Answer:
Step-by-step explanation:
AC= E
AC= CD
BC= EE
Please write the problems I cant see them well
Match the letters with the numbersNote:multiple graphs will be used for each problem. Meaning a problem will have more than one graph to match withNote:it’s like matching the numbers with letters
A function is said to be an odd function if its graph is symmetric with respect to the origin.
Examples of odd functions are;
The odd functions are; C, D E, H, J, K, N
Do anybody know his question?
The table shows the relationship between the participants walking and running for the week's cross-country practices.
Walk (laps) 3 B 15
Run (laps) 5 10 D
Total (laps) A C 40
At this rate, how many laps will the participants walk if the total distance is 32 miles? How many miles will they run?
They will walk 7 laps and run 17 laps for a total of 32 miles.
They will walk 12 laps and run 20 laps for a total of 32 miles.
They will walk 14 laps and run 18 laps for a total of 32 miles.
They will walk 10 laps and run 22 laps for a total of 32 miles.
Question 3(Multiple Choice Worth 2 points)
(Three-Column Tables LC)
PART 2
The data below shows the ratio of brown to green crayons in four kindergarten classrooms.
12 to 20
10 to 25
14 to 35
30 to 75
Which table below correctly shows these ratios in a three-column table?
Brown 20 25 35 75
Green 12 10 14 30
Total 32 35 49 105
Brown 12 10 14 75
Green 20 25 35 30
Total 30 35 44 105
Brown 12 10 14 30
Green 20 25 35 75
Total 32 35 49 105
Brown 12 25 14 30
Green 20 10 35 75
Total 42 35 49 100
Using proportional relationships, it is discovered that they will cover 32 miles overall by walking 12 laps and running 20 laps.
For the second issue, the appropriate response is:
Brown 12 10 14 30
Green 20 25 35 75
Total 32 35 49 105
What is a direct proportional relationship?
In a direct proportional connection, the output variable is determined by multiplying the input variable by the proportionality constant, k, as in the example below:
y = kx.
For the first question, we have that out of a total distance of 8 miles, they:
Walk 3/8 of the distance.
Run 5/8 of the distance.
Hence the proportional relationships for the distances are given as follows:
Walked = 3/8 x Total Distance.
Ran = 5/8 x Total Distance.
For a total distance of 32 miles, the distances walked and ran are given as follows:
Walked: 3/8 x 32 = 3 x 4 = 12 miles = 12 laps.
Ran: 5/8 x 32 = 5 x 4 = 20 miles = 20 laps.
For the second question, we have that the table has to following the given ratios of the first row to the second row, with the third row being the sum of the first two rows, hence the third table is correct.
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Let y represent the total cost of publishing a book (in dollars). Let x represent the number of copies of the book printed. Suppose that x and y are related by the equation y = 1100 + 15x.Answer the questions below.What is the change in the total cost for each book printed?What is the cost to get started (before any books are printed)?
y = 1100 + 15x.
Rewriting
y = 15x+1100
This is in slope intercept form
15 is the slope. It is the change for each x
It is the change for each book
The change in total cost for each book is 15 dollars
The y intercept is 1100. It is the cost when x =0. It is the cost when there are no books printed.
It is the cost to get started
The start up cost is 1100 dollars.
Write the following expression using the fewest possible terms.
the expression quantity three fourths times t minus 5 plus two fifths times t end quantity minus quantity five eighths times t plus 17 end quantity
negative 71 over 40 times t plus negative 12
71 over 40 times t plus negative 22
21 over 40 times t plus negative 12
21 over 40 times t plus negative 22
The computation of the expression using the fewest possible terms is D. 21 over 40 times t plus positive 22
How to calculate the expression?It should be noted that on Mathematics, an expression is used to show the relationship between the variables that are given or illustrated.
In this case, the expression given is illustrated as three fourths times t minus 5 plus two fifths times t end quantity minus quantity five eighths times t plus 17 end quantity.
This will be:
= (3/4t - 5 + 2/5t) - (5/8t + 17)
= (15/20t + 8/20t - 5) - (5/8t + 17)
= 23/20t - 5 - 5/8t + 17
= 46/40t - 5 - 25/70t + 17
= 21/40t + 12
Therefore, the correct option is D.
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need help with this question
E = {2, 4, 6, 10} is a subset of which of the following sets?Question 3 options:C = {1, 2, 3, 4, 5, 7, 8, 9, 10}B = {2, 4, 6}A = {1, 2, 4, 7, 10, 11, 9, 6}D = {4, 6, 8, 10, 12, ...}
Given:
[tex]E=\lbrace2,4,6,10\rbrace[/tex]Required:
We need to find the set that has the subset E.
Explanation:
Recall that a set A is a subset of another set B if all elements of set A are elements of set B.Consider the set A = {1, 2, 4, 7, 10, 11, 9, 6}.
Element 6 from E is not an element of A.
Set E is not a subset of set A.
B = {2, 4, 6}.
7B
Set E is not a subset of set B
D = {4, 6, 8, 10, 12, ...}
2D
D.
C = {1, 2, 3, 4, 5, 7, 8, 9, 10}
Set C has all the elements of E.
C
Final answer:
what is the density of a cube if the mass is 24g
W=2cm
H=2cm
L=2cm
HELP PLEASE!!
Amy will run more than 33 miles this week. So far, she has run 21 miles. What are the possible numbers of additional miles she will run? Use t for the number of additional miles she will run. Write your answer as an inequality solved for t.
Answer:
21 + t > 33
t > 12
Hope this helps!
Step-by-step explanation:
(7x)°
(X/2)
Find the value of the variables
Answer:
X/2 = 12
7X = 168
Step-by-step explanation:
180 = X/2 + 7X
180 = 7.5 X
X = 24
In a country, the highest temperature ever recorded was 110°f and the lowest temperature was -28°f. Find the difference between the highest and lowest temperatures.
We have the temperature points measured on the Fahrenheit scale.
The highest point is 110°f
The lowest point is -28°f
The difference between the two points would be as follows
[tex]110-(-28)=138[/tex]In conclusion, the difference is 138°f
What is the solution, if any, to the inequality 3-|4-n| >1
A. no solution
B. all real numbers
C. n > 2 or n < 6
D. 2 < n < 6
The solution of given inequality 3-|4-n| >1 is 2<n<6.So option D is correct.
An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
The given inequality is 3 - |4-n| > 1
Since |4-n| is the absolute value
Absolute value describes the distance from zero that a number is on the number line, without considering direction. The absolute value of a number is never negative.
So ( 4-n ) may be negative or positive.
For positive value of ( 4-n )
3-( 4-n ) > 1
3-4+n>1
n>2
For negative value of (4-x)
3+( 4-n )>1
3 + 4-n >1
7 - n > 1
-n> 1 -7
-n > -6
n < 6
Hence, 2 < n < 6 i.e. option D is the solution to the inequality 3-|4-n| >1.
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Answer: d
Step-by-step explanation:
Reflection across y=3
In the picture, There is graph with a triangle SNZ. The reflected triangle of y=3 as (1,2),(5,3) and (5,5).
Given that,
In the picture, There is graph with a triangle.
The triangle is SNZ.
We have to find the reflection across y=3.
We have to draw a line on y=3.
On the line y=3,
Z point is there so it will be same that is (5,3).
Now, the point S is on (5,1)
Here, y is 1 that is 3+2=5
So, we take the reflected S point as (5,5)
Now, the point N is on (1,4)
Here, y is 4 that is 3-1=2
So, we take the reflected N point as (1,2).
Therefore, we get the reflected triangle of y=3 as (1,2),(5,3) and (5,5).
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The reflected triangle of y=3 as (1,2),(5,3) and (5,5)
In the picture, there is graph with a triangle SNZ
We have to find the reflection across y=3
A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure
We have to draw a line on y=3
On the line y=3
Z point is there so it will be same that is (5,3).
The point S is on (5,1)
Here, y is 1 that is 3+2=5
Take the reflected S point as (5,5)
The point N is on (1,4)
Here, y is 4 that is 3-1=2
Take the reflected N point as (1,2)
Therefore, the reflected triangle of y=3 as (1,2),(5,3) and (5,5)
The reflected triangle of y=3 as (1,2),(5,3) and (5,5)
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-4 3/5÷1 1/5
Answer in simplest form
Answer: -23/6
Step-by-step explanation:
show all supported calculations. Write an explanation of your conclusion in a complete sentence.
we know that
cost between $25 us and $40 us
Convert 21,130 RP to US
we have
1 RP=0.0147 US
so
Applying proportion
0.0147/1=x/21,130
solve for x
x=21,130*0.0147
x=310.61 US
so
310.61 US is not in the interval [25 US, 40 US]
that means
Is not a mid range hotelComplete the square for y=x^2 - 6x-5?
Answer: y=(x-3)^2 -14
Step-by-step explanation:
use the formula (b/2)^2 to create a new term to complete the square
A gasoline station very near a professional football stadium parks cars on its lot to make money on game days. Last year it charged $4.00 per car and parked 1000 cars. This year it raised the parking price to $5.00 and parked 850 cars. Did the station owner make a good economic decision in raising the parking prices from one year to the next? Explain.
The station owner make a good economic decision in raising the parking prices from one year to the next Ashe made an extra profit of $250.
How to explain the information?From the information, the gasoline station very near a professional football stadium parks cars on its lot to make money on game days. Last year it charged $4.00 per car and parked 1000 cars. The amount made last year will be:
= Amount charged × Number of cars
= $4 × 10000
= $4000
This year it raised the parking price to $5.00 and parked 850 cars. The amount made will be:
= $5 × 850
= $4250
Therefore, the profit made will be:
= $4250 - $4000
= $250
He made a good decision.
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What does x equal? 5(x − 1) = 5x -1
Answer:
Nothing ( 0 )
Step-by-step explanation:
5(x - 1) = 5x - 1
5x - 1 = 5x - 1
5x - 5x = 1 - 1
0 = 0
3. For the number line shown, which
statement is NOT true?
The statement which is not true for the given number line is |c| < d.
What is a number line?The visual representation of numbers on a straight line, either horizontally or vertically, is known as a number line. When numbers are written down on a number line, it is straightforward for humans to compare them and perform basic arithmetic operations on them. One might assume that a number line starts at zero (0). There are only negative numbers to the left of zero and only positive numbers to the right of zero. In other words, as we move to the right on a number line, the value of the numbers increases. This shows that the numbers on the right are more numerous than those on the left.
When any value is written within the mod, it is always considered a positive value.
So, accordingly option (B) |c| < d is the correct answer.
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Your mom has you go to the store to buy oranges and apples. Oranges cost $0.50 each, and apples cost $1.00. Your mom gives you $10. Write an equation that represents the number of oranges and apples you can buy with the money you have.
Let x represent the number of oranges you will buy.
Let y represent the number of apples you will buy.
Determine whether each of these sets is countable or uncountable.
(a) all bit strings that is finite.
(b) all bit strings that is infinite
(c) the real numbers containing a finite number of 1s in their decimal
representation (reminder: the real numbers can contain a infinite
number of 2s or 3s)
(d) the real numbers containing only 1s in their decimal representation
which expression would be added to 5x + 7 to make it equivalent to the expression 9(x + 1) (Here are the answer choices.) A. 4x - 6B. 4x + 2 C. 9x + 1 D. 14x + 8
Let the expression we will add be "A", thus we can write:
[tex]5x+7+A=9(x+1)[/tex]We can use the distributive property on the right hand side and then use a bit algebra to solve for "A". The distributive property is shown below:
[tex]a(b+c)=ab+ac[/tex]Let's do the algebra. The steps are shown below:
[tex]\begin{gathered} 5x+7+A=9(x+1) \\ 5x+7+A=9x+9 \\ A=9x+9-5x-7 \\ A=4x+2 \end{gathered}[/tex]Thus, we need to add 4x + 2 to "5x + 7" to make it equal to "9(x+1)".
The correct answer is:
BFind h (-4), h (0), and h (1).
Answer:
The piecewise function is given below as
[tex]h(x)=\begin{cases}\frac{1}{2}x-2,x<-2 \\ (x-1)^2-1.-2\leq x\leq1 \\ 2,x>1\end{cases}[/tex]Step 1:
To figure out h(-4),
The function that satisfies this is given below as
[tex]\begin{gathered} \frac{1}{2}x-2,x<-2 \\ \text{note:} \\ -4<-2 \end{gathered}[/tex]Therefore,
Substitute the value of x=-4
[tex]\begin{gathered} \frac{1}{2}x-2 \\ h(-4)=\frac{1}{2}(-4)-2 \\ h(-4)=-2-2 \\ h(-4)=-4 \end{gathered}[/tex]Hence,
h( -4 ) = -4
Step 2:
To figure out h(0)
The function that satisfies this condition is given below as
[tex]\begin{gathered} (x-1)^2-1.-2\leq x\leq1 \\ \text{note:} \\ 0<1 \end{gathered}[/tex]Hence,
Substitue the value of x = 0
[tex]\begin{gathered} (x-1)^2-1.-2\leq x\leq1 \\ h(0)=(0-1)^2-1 \\ h(0)=(-1)^2-1 \\ h(0)=1-1 \\ h(0)=0 \end{gathered}[/tex]Hence,
The value for h( 0 ) = 0
Step 3:
To figure out h( 1)
The function that satisfies this condition is given below as
[tex](x-1)^2-1.-2\leq x\leq1[/tex]Substitute x= 1 in the equation below
[tex]\begin{gathered} (x-1)^2-1.-2\leq x\leq1 \\ h(1)=(1-1)^2-1 \\ h(1)=0-1 \\ h(1)=-1 \end{gathered}[/tex]Hence,
The value of h(1) = -1
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
substitute with 10 in the equation
a pole that is 3.3 m tall casts a shadow that is 1.48 m long. At the same time, a nearby tower casts a shadow that is 36.75 m long How tall is the tower
By using trigonometric relations for right triangles, we will see that the height of the tower is 81.92 meters.
How can we find the height of the tower?
First, we know that a pole with a height of 3.3m casts a shadow of 1.48m. We can see the height of the pole and the length of the shadow as the legs of a right triangle, with that, we can get the angle at which the sun hits the pole (this angle is such that the height will be the adjacent cathetus).
Using the trigonometric relation:
tan(a) = (opposite cathetus)/(adjacent cathetus)
We can get:
a = Atan( (opposite cathetus)/(adjacent cathetus))
With taht we can find the angle, where:
opposite cathetus = 1.48m
adjacent cathetus) = 3.3m
Then:
a = Atan(1.48/3.3) = 24.16°
For the tower that angle will be the same one, and again, the height is the adjacent cathetus and the shadow the opposite cathetus, so we can write the same equation than before:
tan(24.16°) = shadow/height.
Solving that for the height we get:
height = shadow/tan(24.16°) = 36.75m/tan(24.16°) = 81.92m
The height of the tower is 81.92 meters.
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