Answer:
[tex]8[/tex]
Step-by-step explanation:
[tex]4(2x-5) \\ \\ 4(2x)-4(5) \\ \\ 4*2=8 \\ \\ 8x-20[/tex]
For this case we have the following expression:
[tex]4 (2x-5) =[/tex]
We simplify according to the steps of Ranger.
We apply distributive property to the terms within parentheses.[tex]4 * (2x) -4 * (5) =[/tex]
We find each product:
[tex]8x-20[/tex]
Answer:
The simplified expression is 8x-20
An "8" is placed in the blank space
I
ESPOO
1. A cylindrical swimming pool has a diameter 32 of feet and a height of 7 feet. About how many gallons of
water can the pool contain? Round your answer to the nearest whole number. (1 ft - 7.5 gal
Answer:
42,223 gallons
Step-by-step explanation:
Find the volume of the pool and then multiply that by the conversion factor 1 ft³: 7.5 gallons.
If the pool diameter is 32 feet, then the pool radius is 16 feet.
The volume here is V = πr²h, or V = π(16 ft)²(7 ft) = 5629.73 ft³
Multiplying this volume by 1 ft³: 7.5 gallons, we get:
(5630 ft³)(7.5 gallons / 1 ft³) = 42,223 gallons
. Let f(x) = x2 and g(x) = x − 3. Evaluate (g ∘ f)(−2). 1 7 20 −20
For this case we have the following functions:
[tex]f (x) = x ^ 2\\g (x) = x-3[/tex]
We must find[tex](g_ {0} f) (x)[/tex]
By definition we have to:
[tex](g_ {0} f) (x) = g (f (x))[/tex]
So:
[tex]g (f (x)) = (x ^ 2) -3 = x ^ 2-3[/tex]
We must evaluate the composite function for [tex]x = -2[/tex]
[tex]g (f (-2)) = (- 2) ^ 2-3 = 4-3 = 1[/tex]
ANswer:
[tex]g (f (-2)) = 1[/tex]
ANSWER
1
EXPLANATION
The given functions are:
[tex]f(x) = {x}^{2} [/tex]
and
[tex]g(x) = x - 3[/tex]
[tex](g \circ \: f)(x) = f(g(x))[/tex]
[tex](g \circ \: f)(x) = g( {x}^{2} )[/tex]
[tex](g \circ \: f)(x) = {x}^{2} - 3[/tex]
We substitute x=-2 to obtain;
[tex](g \circ \: f)( - 2) = {( - 2)}^{2} - 3[/tex]
We simplify to obtain:
[tex](g \circ \: f)( - 2) = 4- 3[/tex]
[tex](g \circ \: f)( - 2) = 1[/tex]
The first choice is correct.
Can you help me with this? Please and thank you.
10 in Actual 35 ft
20 in Actual 70ft
Part B 735 dollars
1) simplify the ratio 15:9:6
2) simplify the ratio 16:20
3) simplify the ratio 36:30
4) simplify the ratio 12:30:24
5) simplify the ratio 12:30
6) simplify the ratio 56:40
7) simplify the ratio 12:4:8
8) simplify the ratio 7.0:4.2
9) simplify the ratio 3:4.5
10) simplify the ratio 1.2:3:2.4
Answer:
1. 5:3:2
2. 4:5
3. 6:5
4. 2:5:6
5. 2:5
6. 7:5
7. 3:1:2
8. 1.0:0.6
9. 1:1.5
10. 0.2:0.5:0.8
Step-by-step explanation:
1. divide everything by 3
2. divide everything by 4
3. divide everything by 6
4. divide everything by 6
5. divide everything by 6
6. divide everything by 8
7. divide everything by 4
8. divide everything by 7
9. divide everything by 3
10. divide everything by 6
Answer::
1. 5:3:2
2. 4:5
3. 6:5
4. 2:5:6
5. 2:5
6. 7:5
7. 3:1:2
8. 1.0:0.6
9. 1:1.5
10. 0.2:0.5:0.8
I hope this helps! :-)
Rationalise the denominator 5 by√7-√5
⇛{5(√7+√5)}/2.
Step-by-step explanation:
Given,
5/(√7-√5)
The denominator is √7-√5.
We know that
The rationalising factor of √c-√a is √c+√a.
Therefore, the rationalising factor of √7-√5 is √7+√5. To rationalise the denominator of 5/(√7-√5), we multiply this by (√7+√5)/(√7+√5).
⇛{5/(√7-√5)}/{(√7+√5)/(√7+√5)}
⇛{5(√7+√5)}/{(√7-√5)(√7+√5)}
⇛{5(√7+√5)}/{(√7)²-(√5)} [∵ (a-b)(a+b)=a²-b²]
⇛{5(√7+√5)}/{(√7*7)-(√5*5)}
⇛{5(√7+√5)}/(7-5)
⇛{5(√7+√5)}/2
Hence, the denominator is rationalised.
Read more:
Similar Question;
rationalise the denominator 1/√20..
https://brainly.com/question/19473806?referrer
PLEASE ANSWER RIGHT AWAY
ANSWER
[tex]a_{7}= - 20[/tex]
EXPLANATION
The sequence is defined recursively by:
[tex]a_{n+1}=-2a_n+4[/tex]
Where
[tex]a_1=1[/tex]
[tex]a_{2}=-2a_1+4[/tex]
[tex]a_{2}=-2(1)+4 = 2[/tex]
[tex]a_{3}=-2a_2+4[/tex]
[tex]a_{3}=-2(2)+4 = 0[/tex]
[tex]a_{4}=-2a_3+4[/tex]
[tex]a_{4}=-2(0)+4 = 4[/tex]
[tex]a_{5}=-2a_4+4[/tex]
[tex]a_{5}=-2(4)+4 = - 4[/tex]
[tex]a_{6}=-2a_5+4[/tex]
[tex]a_{6}=-2( - 4)+4 = 12[/tex]
[tex]a_{7}=-2a_6+4[/tex]
[tex]a_{7}=-2(12)+4 = - 20[/tex]
Data Set A: 3, 5, 7, 10, 10, 4, 7, 5, 8, 10, 6. Find the median Hint: Arrange them in ascending order first!
The median of these numbers is: 7
3,4,5,5,6,7,7,8,10,10,10
Answer:
the median would be 7
Step-by-step explanation:
If each stack of coins has the same height, which stack of coins has the greatest volume?
Answer:
It all depends on the type of coins stacked
The stack of coins with the greatest volume is the one with the largest number of coins and the largest diameter.
Final Answer: The stack of coins with the greatest volume is the one with the largest number of coins and the largest diameter.
To calculate the volume of a stack of coins, we can use the formula for the volume of a cylinder,[tex]V = πr^2h,[/tex] where V is the volume, r is the radius of the coin, and h is the height of the stack.
Since each stack has the same height, we only need to compare the volumes based on the number of coins and their diameter.
First, let's assume the radius of each coin is r and the height of each stack is h. Let's denote the number of coins in each stack as n.
Now, let's calculate the volume for each stack:
1. Stack 1: Volume = [tex]πr^2 * h * n1[/tex]
2. Stack 2: Volume = [tex]πr^2 * h * n2[/tex]
3. Stack 3: Volume = [tex]πr^2 * h * n3[/tex]
Since all stacks have the same height (h), we can disregard it in the comparison.
To compare the volumes, we need to compare the number of coins (n) and the radius of the coins (r).
Let's assume Stack 1 has the largest number of coins, followed by Stack 2 and then Stack 3.
If all stacks have the same number of coins, then the one with the largest diameter (which is the radius times 2) would have the greatest volume.
After calculating the volumes for each stack, we can determine which stack has the greatest volume based on the number of coins and their diameter.
Complete question:
If each stack of coins has the same height, which stack of coins has the greatest volume?
A rectangular pyramid is sliced so the cross section is parallel to its base.
What is the shape of the cross section?
triangle
pentagon
trapezoid
rectangle
It’s a trapezoid would be the answer
Answer:
The answer is below :)
Step-by-step explanation:
1) In a geometric progression, the first term
is 21 and the subsequent terms are
determined by multiplying the preceding
term by 2. What is the sum of the first 25
terms of this sequence?
A. 176,160,763
B. 352,321,525
C. 704,643,051
D. 724,897,062
[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ \cline{1-1} a_1=21\\ r=2\\ n=25 \end{cases} \\\\\\ S_{25}=21\left( \cfrac{1-2^{25}}{1-2} \right)\implies S_{25}=21\left( \cfrac{-33554431}{-1} \right) \\\\\\ S_{25}=21(33554431)\implies S_{25}=704643051[/tex]
What is the surface area of the square pyramid?
Answer:
C. 71.2 in²Step-by-step explanation:
We have the square in the base with side a = 4in and four triangles with base a = 4in and height h = 6.9in.
The formula of an area of a square:
A = a²
Substitute:
As = 4² = 16 in²
The formula of an area of a triangle:
A = (ah)/2
Substitute:
At = [(4)(6.9)]/2 = 27.6/2 = 13.8 in²
The Surface Area:
S.A. = As + 4At
Substitute:
S.A. = 16 + 4(13.8) = 16 + 55.2 = 71.2 in²
3/13=×/5 solving for x
Answer:
x = 15/13
Step-by-step explanation:
3/13 = x/5
Using cross products
13*x = 3*5
13x = 15
Divide each side by 13
13x/13 = 15/13
x = 15/13
Your phone service allows you to add international long distance to your phone. The cost is a $15 flat fee and then $.25 a minute for calls made. Write an explicit function rule describing your monthly cost for international calls.
C=$0.25m+$15 because 0.25 is the slope and 15 is the y-intercept.
C stands for Cost
M stands for Minute
Final answer:
The cost of international calls can be calculated using the explicit function rule C(m) = 15 + 0.25m, where m is the number of minutes and $15 is the flat fee.
Explanation:
The student asks for an explicit function rule that represents the monthly cost of international calls given a $15 flat fee and a rate of $0.25 per minute. To address this, we introduce a function where C(m) represents the total cost of making international calls for m minutes in a month.
The cost function is C(m) = 15 + 0.25m. The term $15 flat fee is the initial cost regardless of call duration, and $0.25 per minute is the variable rate that depends on the total minutes used.
If for example, a user talked for 100 minutes, the calculation would be C(100) = 15 + 0.25(100) = 15 + 25 = $40.
please I don’t understand this I need help #2
Answer:
True for B)y=-4x^2+9
Step-by-step explanation:
The a part of the equation is negative (-4x^2), and this quadratic function has a maximum, which means it opens down not up.
(I hope this helps)
Find the least common denominator for these two rational expressions Please!!!!
Answer:
(x + 2)²(x - 1)
Step-by-step explanation:
Factorise the denominators of both fractions
x² + 4x + 4 ← is a perfect square = (x + 2)²
x² + x - 2 = (x + 2)(x - 1)
The fractions can be expressed as
[tex]\frac{x(x-1)}{(x+2)^2(x-1)}[/tex] and [tex]\frac{2(x+2)}{(x+2)^2(x-1)}[/tex]
least common multiple is (x + 2)²(x - 1)
Which of these pairs of events are dependent?
a. You flip a coin and get tails. You flip it a second time and get heads.
b. You pull your friend's name out of a hat that holds 20 different names, replace
name, then draw out your friend's name again.
c. You spin a spinner divided into five equal parts and is numbered 1-5. You get a 3 on the first spin, and then spin again and get a 2 on the second spin.
d. You remove a black sock from a drawer without looking, then remove another black
sock.
Answer:
d
Step-by-step explanation:
a, b, and c are independent, because they don't necessarily affect the probability of each other.
In summary, the pair of events that are dependent is drawing a black sock from a drawer and then drawing another without replacement. This is because the first event changes the conditions for the second, affecting its probability.
Explanation:Whether two events are dependent or independent affects the calculation of their probability. Independent events have no impact on the likelihood of each other occurring, while dependent events do.
Event a (flipping a coin twice) involves independent events because the outcome of the first flip does not affect the second flip's outcome.Event b (drawing a friend's name from a hat, replacing it, and drawing again) also involves independent events as the outcome of the first draw is not affected by the second, thanks to the replacement.Event c (spinning a numbered spinner twice) is another example of independent events since the result of the first spin does not affect the second spin.Event d (removing black socks from a drawer one after another without replacement) involves dependent events because the outcome of the first draw affects the probability of the second; removing one sock changes the total number of socks, which affects the chances of drawing a black sock again.Thus, Event d is the pair of dependent events.
Jack invested $5,280 in a regular savings account that paid
simple interest at a rate of 1.15% per year. How much was
his investment worth in one year?
$6,072
$60.72
$5,340.72
$5,281.15
$5887.20
Final answer:
To calculate the value of Jack's investment after one year, we can use the formula for simple interest: Simple Interest = Principal x Rate x Time. Plugging in the values, we find that Jack's investment will be worth $5,340.72 after one year.
Explanation:
To calculate the value of Jack's investment after one year, we can use the formula for simple interest:
Simple Interest = Principal x Rate x Time
In this case, the principal is $5,280, the rate is 1.15% (which can be written as 0.0115), and the time is one year. Plugging in these values, we get:
Simple Interest = $5,280 x 0.0115 x 1 = $60.72
To find out the total value of the investment after one year, we need to add the simple interest to the principal amount:
Total Value = Principal + Simple Interest = $5,280 + $60.72 = $5,340.72
Therefore, Jack's investment will be worth $5,340.72 after one year.
What is the point-slope form of a line that has a slope of –4 and passes through point (–3, 1)?
Answer:
[tex]\large\boxed{y-1=-4(x+3)}[/tex]
Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have m = -4 and the point (-3, 1). Substitute:
[tex]y-1=-4(x-(-3))\\\\y-1=-4(x+3)[/tex]
Answer:
y-1=-4[x-(-3)]
Step-by-step explanation:
Please help will give brainliest
ANSWER
r is not a set of ordered pair
EXPLANATION
A relation is a correspondence between two sets.
In a relation, the elements from one set set (domain) maps on to the elements in a second set(co-domain).
The relation can then be written as an ordered pair (x,y).
The given listing is
r={√3,√5,√7, √13}
This is not an ordered pair so it cannot be a relation.
The third choice is correct.
Answer:
Choice C is correct, r is not a set of ordered pairs
Step-by-step explanation:
A relation between sets of data is a collection of ordered pairs which contain one object from each set. If the element x is from the first set and its corresponding object y from the second set, then the objects are said to be related if the ordered pair (x,y) is in the relation.
X comprises of the domain while Y makes up the range.
Therefore, r is not a relation since it is not a set of ordered pairs.
What set of transformations
Set of transformations is a set conditioned by a function that transforms element from definition set to transformation set.
[tex]f: A\longrightarrow B[/tex], where A is definition set and B is transformation set.
Here is an example.
You are given definition set [tex]A=\{1, 2, 3\}[/tex] and a function [tex]f(x)=x^2[/tex]. To calculate which elements are in transformation set we write [tex]f(A)=\{1, 2, 3\}^2={1, 4, 9}\Longrightarrow\boxed{B=\{1, 4, 9\}}[/tex] and B is now the transformation set of definition set A that is conditioned by function f.
Hope this helps.
r3t40
Specify the domain for he function !!! A-B-C-D 10 points. MATH 3
ANSWER
[tex]( - \infty , - \frac{4}{3} ) \cup( \frac{1}{2} , \infty )[/tex]
EXPLANATION
The given function is
[tex]f(x) = \sqrt{ \frac{2x - 1}{3x + 4} } [/tex]
The domain refers to all values of x for which f(x) is defined.
This function is defined if
[tex] \frac{2x - 1}{3x + 4} > 0[/tex]
This implies that
[tex]x \: < \: - \frac{4}{3} \: or \: x \: > \: \frac{1}{2} [/tex]
Or
[tex]( - \infty , - \frac{4}{3} ) \cup( \frac{1}{2} , \infty )[/tex]
Use the graph of the polynomial function to find the factored form of the related polynomial. Assume it has no constant factor.
Answer:
A. (x - 1)(x - 8)
Step-by-step explanation:
By looking at the graph, we can see that the polynomial has roots at x = 1 and 8. This means that the function in factored form would look like (x - 1)(x - 8).
Answer:
A) (x - 1)(x - 8)
Step-by-step explanation:
Apex
On Monday, Kevin wrote a check for $575 to pay his rent. On Tuesday, he deposited at
$638. On Friday, he wrote checks for $75 for groceries and S266 for a car repair Wasche
the overall change in his checking account balance for the week, in dollars?
a. -278
b. -916
c. -1554
d. --178
Answer:
a
Step-by-step explanation
-(575+266+75)+638
The first steps in determining the perimeter of triangle ABC are shown.
To the nearest whole unit, what is the perimeter of triangle ABC?
Answer: [tex]P=14units[/tex]
Step-by-step explanation:
The perimeter of a triangle is the sum of the lenghts of its sides.
Given the triangle ABC , its perimeter will be:
[tex]P=AB+BC+CA[/tex]
Then, you know that the lenghts of the sids of the triangle ABC are:
[tex]AB=3units\\BC=5units\\CA=\sqrt{(3)^2+(-5)^2}=\sqrt{9+25}=\sqrt{34}=5.83units[/tex]
Therefore, to find the perimeter of this triangle, you need to substitute these lengthts into the formula [tex]P=AB+BC+CA[/tex].
So, the perimeter of the triangle ABC is:
[tex]P=3units+5units+5.83units=13.83units[/tex]
To the nearest whole unit is:
[tex]P=14units[/tex]
Answer:
14 units
Step-by-step explanation:
.
a rhombus as an area of 72 ft and the product of the diagonals is 144. What is the length of each diagonal?
A = (1/2)(x)(y)
Let x = diagonal 1
Let y = diagonal 2
The product of xy = 144.
This means that x = 12 and y = 12.
So, 12 • 12 = 144
Each diagonal is 12 feet.
Prove:
72 feet = (1/2)(12)(12) feet
72 feet = (1/2)(144) feet
72 feet = 72 feet
To find the length of each diagonal of the rhombus, we'll use the relationship between the area of a rhombus and its diagonals. The formula for the area (A) of a rhombus in terms of its diagonals (d1 and d2) is given by:
\[ A = \frac{d1 \cdot d2}{2} \]
Additionally, we are given the product of the diagonals, which means:
\[ d1 \cdot d2 = 144 \]
Since we are also given the area of the rhombus, which is 72 square feet, we can write:
\[ 72 = \frac{d1 \cdot d2}{2} \]
\[ 144 = d1 \cdot d2 \]
We have two equations with two variables, which we can solve simultaneously. However, in this case, since both equations involve the product of d1 and d2, we can use the given product directly. We know that:
\[ 2 \cdot 72 = 144 \]
\[ d1 \cdot d2 = 144 \]
We can use a property of numbers that states that the product of two numbers is equal to the square of their average if and only if the two numbers are the same. However, here we are interested in finding two different numbers whose product is 144.
We can do this by breaking down 144 into pairs of factors and then checking which pair would satisfy the condition that their product divided by 2 is equal to 72. The pair of factors of 144 that add up to 144 when multiplied and divide to 72 when halved are the actual lengths of the diagonals.
One way to determine the pair is through the process of factoring 144:
\[ 144 = 1 \times 144 \]
\[ 144 = 2 \times 72 \]
\[ 144 = 3 \times 48 \]
\[ 144 = 4 \times 36 \]
\[ 144 = 6 \times 24 \]
\[ 144 = 8 \times 18 \]
\[ 144 = 9 \times 16 \]
\[ 144 = 12 \times 12 \]
We need to find two different factors since a rhombus's diagonals are not equal. Among the listed factors, the pair 18 and 8 satisfy the condition because:
\[ \frac{18 \cdot 8}{2} = \frac{144}{2} = 72 \]
So, the lengths of the diagonals of the rhombus are 18 feet and 8 feet.
Over the past 15 years, a business owner has made at most $4,000 in profits each week .Which graph represents the business owner's possible profits each week ? I chose the last one , am I correct????
The graph fourth represents the inequality x ≤ 4000 if in the past 15 years, a business owner has made at most $4,000 in profits each week option fourth is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.
We have:
Over the past 15 years, a business owner has made at most $4,000 in profits each week.
So the peak value is $4,000
Let's suppose the business owner earns $x profit each week, then we can frame an inequality:
x ≤ 4000
From the above inequality, the value of x will be:
x belongs to (0, 4000)
Thus, the graph fourth represents the inequality x ≤ 4000 if in the past 15 years, a business owner has made at most $4,000 in profits each week option fourth is correct.
Learn more about the inequality here:
brainly.com/question/19491153
#SPJ2
If f(x) = -7x+2 and g(x) = square root of x+3,
what is (fºg)(-2)?
Answer:
(fog)(-2)=-5
Step-by-step explanation:
Given
f(x)= -7x+2
and
g(x)= √(x+3)
For finding (fog)(-2), we have to find (fog)(x) first
In order to find (fog)(x) we will put the value of g(x) in f(x) in place of x.
(fog)(x)= -7g(x)+2
Putting the value of g(x)
(fog)(x)= -7√(x+3)+2
We have to find (fog)(-2), so we have to put at the place of x in the composition
(fog)(-2)= -7√(-2+3)+2
(fog)(-2)= -7√1+2
= -7(1)+2
= -7+2
=-5
So,
(fog)(-2)=-5
For this case we have the following equations:[tex]f (x) = - 7x + 2\\g (x) = \sqrt {x + 3}[/tex]
We must find [tex](f_ {o} g) (x):[/tex]
By definition of composition of functions we have to:
[tex](f_ {o} g) (x) = f (g (x))[/tex]
So:
[tex](f_ {o} g) (x) = - 7 \sqrt {x + 3} +2[/tex]
Now, we find f (g (-2)):
[tex](f_ {o} g) (- 2) = - 7 \sqrt {-2 + 3} + 2 = -7 \sqrt {1} + 2 = -7 + 2 = -5[/tex]
ANswer:
-5
I WILL GIVE BRANLY A librarian kept track of the kinds of books that boys and girls checked out in one day. Which graph best represents this data?
Answer:
You did not give me any graphs but I've dealt with this question and the answer is: The Double Bar Graph if you have the graph that was put for my answer. Good luck, hope this helps. Double Bar Graph information: Vertical double-bar graph with title Books Checked Out. Key shows grey equals boys and pink equals girls. Data graphed is Biography 8 boys and 10 girls, Mystery 18 boys and 15 girls, Science 14 boys and 11 girls, and Sports 12 boys and 14 girls.
Heres the graphs xd (I have the same test)
The first four terms of a sequence are shown. 16, 48, 144, 432, ...
What is the common ratio, r, for this sequence?
new question
What is the average rate of change of the function below on the interval from x=-1 and x=1?
g(x)=50(12)x
If necessary, write your answer as a decimal.
New Question
Which function’s graph has a y-intercept of 1?
Question 3 options:
h(x)=0.5(2)x+0.5
h(x)=(0.5)x+1
h(x)=5(2)x
h(x)=5(0.5)x+0.5
New Question
Which ordered pairs lie on the graph of the exponential function f(x)=2(3)x?
Choose ALL correct answers.
Question 1 options:
(2,18)
(0,2)
(−1,1)
(3,56)
Answer:
First question: The common ratio r is 3
Second question: The average rate of change is 297.92
Third question: The function's graph of h(x) = 0.5(2^x) + 0.5 has a
y-intercept of 1
Fourth question: The ordered pairs lie on the graph of f(x) are (2 , 18)
and (0 , 2)
Step-by-step explanation:
First question:
* Lets revise the rule of the geometric sequence
- There is a constant ratio between each two consecutive numbers
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
* General term (nth term) of a Geometric sequence:
- U1 = a , U2 = ar , U3 = ar2 , U4 = ar3 , U5 = ar4
- Un = ar^n-1, where a is the first term , r is the constant ratio
between each two consecutive terms and n is the position
of the term in the sequence
* Now lets solve the question
∵ The sequence is 16 , 48 , 144 , 432 , ................
∵ a = 16
∵ ar = 48
∴ r = 48/16 = 3
∴ The sequence is geometric withe common ratio 3
* The common ratio r is 3
Second question:
* Lets revise the average rate of change of a function
- When you calculate the average rate of change of a function,
you are finding the slope of the secant line between the two points
on the function
- Average Rate of Change for the function y = f (x) between
x = a and x = b is:
change of y/change of x = [f(b) - f(a)]/(b - a)
* Now lets solve the problem
∵ g(x) = 50(12^x), where x ∈ [-1 , 1]
∵ a = -1 and b = 1
∵ f(-1) = 50(12^-1) = 50/12
∵ f(1) = 50(12^1) = 600
∴ Average Rate of Change = [600 - 50/12]/[1 - (-1)]
∴ Average Rate of Change = [595.8333]/[2] = 297.92
* The average rate of change is 297.92
Third question:
* Lets talk about the y- intercept
- When any graph intersect the y-axis at point (0 , c), we called
c the y-intercept
- To find the y- intercept, substitute the value of x in the
function by zero
* Now lets check which answer will give y- intercept = 1
∵ h(x) = 0.5(2^x) + 0.5 ⇒ put x = 0
∴ h(0) = 0.5(2^0) + 0.5 = 0.5(1) + 0.5 = 1
∵ h(x) = (0.5)^x + 1 ⇒ put x = 0
∴ h(0) = (0.5)^0 + 1 = 1 + 1 = 2
∵ h(x) = 5(2^x) ⇒ put x = 0
∴ h(0) = 5(2^0) = 5(1) = 5
∵ h(x) = 5(0.5)^x + 0.5
∴ h(0) = 5(0.5)^0 + 0.5 = 5(1) + 0.5 = 5.5
* The function's graph of h(x) = 0.5(2^x) + 0.5 has a y-intercept of 1
Fourth question:
* Lets study how to find a point lies on a graph
- When we substitute the value of x of the point in the function
and give us the same value of y of the point, then the point
lies on the graph
* Now lets solve the problem
∵ f(x) = 2(3)^x
∵ The point is (2 , 18) ⇒ put x = 2
∴ f(2) = 2(3)² = 2(9) = 18 ⇒ the same y of the point
∴ The point (2 , 18) lies on f(x)
∵ The point is (0 , 2) ⇒ put x = 0
∴ f(0) = 2(3)^0 = 2(1) = 2 ⇒ the same y of the point
∴ The point (0 , 2) lies on f(x)
∵ The point is (-1 , 1) ⇒ put x = -1
∴ f(-1) = 2(3)^-1 = 2(1/3) = 2/3 ⇒ not the same y of the point
∴ The point (-1 , 1) does not lie on f(x)
∵ The point is (3 , 56) ⇒ put x = 3
∴ f(3) = 2(3)³ = 2(27) = 54 ⇒ not the same y of the point
∴ The point (3 , 56) does not lie on f(x)
* The ordered pairs lie on the graph of f(x) are (2 , 18) and (0 , 2)
Answer:
3eeddw
Step-by-step explanation:
if f(x)=5x+7 and g(x)=√x+6, which statement is true?
A.) 9 is not in the domain of f ° g
B.) 9 is in the domain of f ° g
Answer:
Statement b is true; statement a is false
Step-by-step explanation:
Best to write out (f o g)(x) and then determine its domain:
"(f o g)(x)" indicates that g(x) is used as the input to f(x):
(f o g)(x) = 5(√x+6) + 7, or 5√x + 30 + 7, or 5√x + 37.
The domain of this composite function is [0, infinity).
Thus, statement b is true: "9 is part of the domain of (f o g)(x) = 5(√x+6) + 7"
To determine which statement is true, we will need to look at the functions f(x) and g(x) and their composition (f ° g)(x), which means we plug g(x) into f(x).
The given functions are:
f(x) = 5x + 7
g(x) = √x + 6
The composition of the functions (f ° g)(x) is f applied to g(x), which would be:
(f ° g)(x) = f(g(x)) = f(√x + 6)
This simplifies to:
(f ° g)(x) = 5(√x + 6) + 7
To be able to plug a number into (f ° g)(x), it must first be in the domain of g(x), and then the result of g(x) must be in the domain of f(x). The domain of g(x) is defined by the set of all x for which g(x) is real and defined. Since g(x) includes a square root, x must be non-negative (x ≥ 0). For f(x), the domain is all real numbers since linear functions are defined for all real x.
So, to determine if 9 is in the domain of (f ° g)(x), we will do the following:
1. Verify if 9 is in the domain of g(x). Since the domain of g(x) includes all x ≥ 0 and 9 ≥ 0, 9 is in the domain of g(x).
2. Calculate g(9) to determine if the output is within the domain of f(x):
g(9) = √9 + 6
g(9) = 3 + 6 (because √9 is 3)
g(9) = 9, which is a real number and thus in the domain of f(x).
3. Since we have that g(9) is in the domain of f(x), we can compute (f ° g)(9):
(f ° g)(9) = f(g(9))
(f ° g)(9) = f(9)
(f ° g)(9) = 5 * 9 + 7
(f ° g)(9) = 45 + 7
(f ° g)(9) = 52
Thus, we have found that 9 is in the domain of g(x), and that (f ° g)(9) is defined and equals 52. This means that statement B, "9 is in the domain of f ° g," is true.