The percentage increase is 22.72%
How to determine the percentage increase?The given parameters are:
Initial = 440 coins
Final = 540 coins
The percentage increase is calculated as:
%Increase = (Final - Initial)/Initial * 100%
So, we have:
%Increase = (540 - 440)/440 * 100%
Evaluate the difference
%Increase = 100/440 * 100%
Evaluate the quotient
%Increase = 0.2272 * 100%
Evaluate the product
%Increase = 22.72%
Hence, the percentage increase is 22.72%
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f(x)=√x - 8. Find f¹(x) and its domain.
A. f¹(x) = x² +8; x≥ −8
-1
OB. f¹(x) = x² +8; x20
O c. f¹(x) = (x + 8)²; x≥ −8
O D. f-¹ (x) = (x+8)²; x≥0
The inverse function is [tex]f^{-1} = (x + 8)^2[/tex], and the domain is the set of all real numbers equal to or larger than -8. So the correct option is C.
How to find the inverse function?Remember that two functions are inverses if and only if:
[tex]f( f^{-1}(x)) = x\\f^{-1}(f(x)) = x[/tex]
Here we have:
[tex]f(x) = \sqrt{x} - 8[/tex]
Then we want to have:
[tex]f(f^{-1}(x)) = \sqrt{f^{-1}(x)} - 8 = x[/tex]
Solving that for the inverse function, we get:
[tex]f^{-1} = (x + 8)^2[/tex]
Now, how to get the domain. The domain of the inverse function is equal to the range of the original function.
[tex]f(x) = \sqrt{x} - 8[/tex]
The range of f(x) is the set of all real numbers larger or equal than -8 (because the smallest value that x can take is 0).
Then the domain of the inverse function is the set of all real numbers equal to or larger than -8.
The correct option is C.
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Find the highest common factor [HCF] of 10 and 17
Answer
Step by step explanation
Solve these 2 problems hurrry!!!!!
Answer:
question 3: n is bigger than or equal to 0
question 5: n is bigger than or equal to 0 (the same as question 3)
Step-by-step explanation:
solve the same way as a equation. just remember the symbols
HELP ASAP/NOW....NO JOKES OR LINKS!!!!!!
what is the vale of the expression -2x^2-4x+10 when x= -3
A. -20
B. 16
C. 40
D. 4
Answer:
D. 4
Step-by-step explanation:
Given expression:
[tex]-2x^2-4x+10[/tex]
To find the value of the expression when x = -3, substitute x = -3 into the expression:
[tex]\implies -2(-3)^2-(-3)x+10[/tex]
Apply exponent rule [tex](-a)^2=a^2[/tex]:
[tex]\implies -2(3^2)-4(-3)+10[/tex]
[tex]\implies -2(9)-4(-3)+10[/tex]
[tex]\implies -18-4(-3)+10[/tex]
Apply rule [tex]-(-a)=a[/tex] :
[tex]\implies -18+(4)(3)+10[/tex]
[tex]\implies -18+12+10[/tex]
Add/subtract from left to right:
[tex]\implies -6+10[/tex]
[tex]\implies 4[/tex]
Let's find
-2x²-4x+10-2(-3)²-4(-3)+10-2(9)+12+10-18+224simplify -9(5 - 2) - 111÷3 show all work
Answer:
-64
Step-by-step explanation:
use PEMDAS order : Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)
-9(5 - 2) - 111÷3 =
-9(3) - 111÷3 =
-27 - 111÷3 =
-27 - 37 =
-64
Determine the solution to the system of equations graphed below and explain your reasoning and complete sentences
g(x)=-2x-3
f(x)= |x+1|-4
Answer:
(x, y) = (0, -3)
Step-by-step explanation:
On a graph, the solution to a system of equations is the set of points where the graphs of the equations intersect.
__
solutionThe graphs for this system of equations intersect at the point (0, -3). That point is the only solution for this system of equations.
The solution is (x, y) = (0, -3).
Two linear equations are shown.
C
654321₁
4
66
y=1/3x+2
y=4/3x-5
What is the solution to the system of equations?
O (7.4)
0 (7.33)
O
0 (8)
O
O (9.7)
Answer: Option (2)
Step-by-step explanation:
Setting the equations equal to each other,
[tex]\frac{1}{3}x+2=\frac{4}{3}x-5\\\\7=x[/tex]
If x=7, then [tex]y=\frac{7}{3}+2=\frac{13}{3}[/tex]
Jack have 34 toy cars, Mike says he have 3 times more than Jack's toy cars. How many toy cars does Mike have?
Answer:102
Step-by-step explanation:
34 x 3 = 102
Answer:
102
Step-by-step explanation:
Since Jack has 34 toy cars and Mike has 3 times more than Jack's toys, we should multiply 34 with 3 to get the answer.
34 * 3 = 102
So, this means that Mike has 102 toy cars.\
Hope this helps :)
7. Holly plays pool on Sundays. She pays $6.50 for admission and $3.50 for
each round she plays. Which expression can be used to determine how
much she pays if she plays x rounds of pool?
Answer:
3.50x+6.50=y
Step-by-step explanation:
Fill in the blank. In the triangle below, x= Round your answer to two
decimal places.
Answer:
The answer is 44.80 degrees
Step-by-step explanation:
First you want to find z
z = 180-(52+90)=38
and then try to determine which formula will try to give you x = Tan
Tan = Opposite/ Adjacent
Tan(38)=35/x
x=35/Tan(38)
x=44.80
PLEASE HELP IT IS DUE AT 11:15
Answer:
35, 31, 25, 18
Step-by-step explanation:
10 x 7/2 = 35
10 + 7 + 14 = 31
8 1/3 x 6/2 = 25
4 1/3 + 5 1/3 + 8 1/3 = 18
Evaluate 5x³ + 2 for x = -1.
0 -3
04
06
0-7
Answer:
-3
Step-by-step explanation:
5x³ + 2 , when x = -1
5(-1)³ + 2
= -5 + 2
= -3
Answer:
-3
(first option listed)
Step-by-step explanation:
we know that 5x³ + 2 is our expression
we want to "evaluate" (find/solve for) when x = -1
we can do this by plugging in -1 to the expression:
5x³ + 2 {note, x = -1}
5(-1)³ + 2 {-1³ = -1}
5(-1) + 2
(-5) + 2
-5 + 2 = - 3
so, when x = -1, the statement is equivalent to -3
hope this helps! :)
In calm water, the motorboat of Jana is moving at the speed of 16.5km/h. On a river, because of the current, the boat moves faster down the river only by raising it. Jana went up the river in 5 hours and the decent in only 2 hours. What is the speed of the current?
Answer: 707 km/h
Step-by-step explanation:
let c = speed of current
16.5 + c = speed of sailboat downstream
16.5 - c = speed of sailboat upstream
distance = travel time * speed
﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋﹋
2(16.5 + c) = 5(16.5 - c)
33 + 2c = 82.5 - 5c
7c = 49.5
c = 7.07 km/h
Which absolute value function, when graphed, will be wider than the graph of the parent function, f(x) = |x|?
f(x) = |x| + 3
f(x) = |x − 6|
f(x) = |x|
f(x) = 9|x|
There is no absolute value function when graphed, will be wider than the graph of the parent function f(x) = |x|
What is an absolute value function?An absolute value function is a function such that,
[tex]|x|=-1 when x\geq 0 and |x|=1 when x\leq 0[/tex]
For the given example,
We have been given a parent function f(x) = |x|
We need to find the absolute value function, when graphed, will be wider than the graph of the parent function.
Consider the graph of all absolute value functions.
The graph of f(x) = |x| + 3 is represented blue color.
The graph of f(x) = |x − 6| is represented green color.
The graph of f(x) = |x| is represented red color.
The graph of f(x) = 9|x| is represented violet color.
From this graph, we can observe that,
f(x) = |x| + 3 is as wise as the parent absolute value function f(x) = |x| translated up by 3 units.
Similarly, the function f(x) = |x - 6| is as wise as the parent absolute value function f(x) = |x| translated right by 6 units.
This means, there is no absolute value function when graphed, which will be wider than the graph of the parent function f(x) = |x|
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Answer:
I believe the answer is C. F(x)= 1/3|x|
Step-by-step explanation:
i hope this helps.
Suppose as part of a national study of economic competitiveness a marketing research firm randomly sampled 200 adults between the ages of 27 and 35 living in metropolitan seattle and 180 adults between the ages of 27 and 35 living in metropolitan minneapolis. each adult selected in the sample was asked, among other things, whether they had a college degree. from the seattle sample 66 adults answered yes and from the minneapolis sample 63 adults answered yes when asked if they had a college degree. based on the sample data, can we conclude that there is a difference between the population proportions of adults between the ages of 27 and 35 in the two cities with college degrees
No we cannot conclude that there is a difference between the population proportion of adults between the ages of 27 and 35 in the two cities.
How to solve for the population proportionFor Seattle
66/200 = 0.33
For Minneapolis
63/180
= 0.35
We have to form our hypothesis
H0: p1 = p2
H1: p1 ≠ p2
We solve for the test statistic
z = (p1-p2)/√(p1*(1-p1)/n1+p2x(1-p2)/n2)
The calculation is given as -0.41
The excel output is given in the attachment
=-0.41
At a significance level of 0.1, the level of acceptance is at -1.645 and 1.645. The value of the test stat can be found here.
Since Z=-0.41 is between -2.58 and 2.58, we do not reject H0.
Hence we fail to reject the null hypothesis.
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Can someone please help
Answer:
Option 1
Step-by-step explanation:
Angle bisector:
Angle bisector is a line that divides the angle into two equal angles.
⇒ ∠KLM = ∠MLN
Kayla has 18 bottles of bubbles. She wants to give 2 bottles to each of her 6 friends. How many bottles will she have left over? Which expression solves the problem?
Expressions:
(18/2)/6
(18/2)+6
(18*2)-6
(18*2)+6
Answer: she would have 6 bottles left, (18/2)/6
Step-by-step explanation:
she has 18 bottles, when you divide it by two, she could give two bottles to 9 people. but, she only wants to give it to 6 friends. meaning that she would be left with 3 pairs of bubbles. as in, 6 bottles.
Use the factorization to find the values of x for which p(x) = 0. (x – 1)(x 1)(x 5) = 0 x – 1 = 0, so x = x 1 = 0, so x = x 5 = 0, so x =
Answer: (x – 1)(x + 1)(x + 5) = 0
x – 1 = 0, so x = 1
x + 1 = 0, so x = -1
x + 5 = 0, so x = -5
Find the remainder when f(X)=2x^3+2x^2-3x-3 is divided by X-2
The remainder when f(x) = 2x³ + 2x² - 3x - 3 is divided by x - 2 is 15.
We know that the remainder theorem states that if a polynomial p(x) is divided by a linear polynomial q(x) whose zero is x = a, then the remainder is given by r = p(a).
Here p(x) = f(x) = 2x³ + 2x² - 3x - 3 and q(x) = x - 2. First, we have to find the zero of q(x).
Now, q(x) = 0
i.e. x - 2 = 0
i.e. x = 2.
So, the zero of q(x) is 2, i.e. a = 2.
Then by the remainder theorem,
r = p(a) = f(2) = 2(2)³ + 2(2)² - 3(2) - 3 = 2 × 8 + 2 × 4 - 6 - 3 = 16 + 8 - 9 = 16 - 1 = 15
We can conclude that the remainder when f(x) = 2x³ + 2x² - 3x - 3 is divided by x - 2 is 15.
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Alexa needs 20.5 pints of blueberries to
jam. She picked 7.75 pints on Friday and
pints on Saturday. How many more pints
she need to pick?
Answer:
Your question does not make much sense but that was only because you were missing one variable which was 4.25 which was what you picked up on Saturday. but anyways you just add 7.75 and 4.25 and you'd end up with 12 so she has 12 pints of the blueberries she needs and to find out the remanding you just subtract from the 20.5 but its better to look at it like 20.50 because that's what it is and then you subtract 12 from 20.50 and you are left with 8.50.
Your answer is 8.5
The sum of two numbers is 48. If one number is three more than twice the second number, which of the following is the
smaller number?
O 24
O 15
O 30
O 33
Answer:
15
Step-by-step explanation:
"one number is three more than twice the second number"
15 * 2 = 30
30 + 3 = 33
15 + 33 = 48
Answer:
15
Step-by-step explanation:
The key to most problems of this type is carefully translating the word problem into math ... an equation.
"The sum of two numbers is 48."
"Sum": Add
"two numbers": we'll need two numbers... let's call them x & y
"is": =
"48": 48
So, the first sentence means: [tex]x+y=48[/tex]
Note that we have two unknowns here. To solve for them, we'll need another equation... at least as many equations as unknowns (2 unknowns, needs 2 equations).
"If one number is three more than twice the second number..."
"one number": x
"is": =
"three more than": +3
"twice": 2*
"the second number": y
So, the second sentence introductory clause means: [tex]x=2y+3[/tex]
Systems of equationsWe have a system of equations. We need as many equations as we have unknowns. We currently have two equations, and two unknowns. Let's try to solve the system:
[tex]x+y=48[/tex]
[tex]x=2y+3[/tex]
There are two main methods to solve systems of equations: Substitution & Elimination
To use the Substitution Method, we'll need to isolate one of the variables in one of the equations, substitute, and solve.
To use the Elimination Method, we'll need to align like terms, find or build matching coefficients with opposite signs, add to eliminate, and solve.
Given that equation 2 already has x isolated, this system is already ready to use the Substitution method, so let's do that.
Solving a system with the Substitution Method[tex]x+y=48\\x=2y+3[/tex]
[tex](2y+3) + y = 48[/tex]
[tex]2y+3 + y = 48[/tex]
[tex]3y+3 = 48[/tex]
[tex]3y= 45[/tex]
[tex]y= 15[/tex]
To find x, substitute back into one of the equations: Equation 2 already has x isolated, so it will be easy to solve for x.
[tex]x=2(15)+3[/tex]
[tex]x=30+3[/tex]
[tex]x=33[/tex]
So the solution we found is x=33 and y=15.
Check to make sure it satisfies the original conditions:The sum of the numbers is 48:
[tex]x+y=(33)+(15)\\x+y=48[/tex]
One number is three more than twice the second number
[tex]x=2y+3[/tex]
[tex](33)\text{ ?=? }2(15)+3[/tex]
[tex]33=33[/tex]
Our answer satisfies all of the original conditions, so our answer works.
Answering the questionThe question finally asks, "...which of the following is the smaller number?"
Of the two numbers, the smaller number is 15.
L
N
(x-4) in. O
(x-3) in.
(x + 2) in.
x in.
K
Which value of x would make NO || KJ?
1
6
08
O 10
Answer:
x = 8
Step-by-step explanation:
[tex]\sf If\:\: \overline{NO} \parallel \overline{KJ}\:\:then\:\: \triangle LNO \sim\triangle LKJ[/tex]
Therefore:
[tex]\implies \sf \overline{LN} : \overline{LO} = \overline{LK} : \overline{LJ}[/tex]
[tex]\implies (x-3):(x-4)=(x-3)+(x+2):(x-4)+x[/tex]
[tex]\implies \dfrac{x-3}{x-4}=\dfrac{2x-1}{2x-4}[/tex]
[tex]\implies (x-3)(2x-4)=(2x-1)(x-4)[/tex]
[tex]\implies 2x^2-10x+12=2x^2-9x+4[/tex]
[tex]\implies -10x+12=-9x+4[/tex]
[tex]\implies 12=x+4[/tex]
[tex]\implies x=8[/tex]
Can you answer this and explain it please! for 100 points
Answer:
D) -12
Step-by-step explanation:
[tex]3(x-4)+(2-x)-x^2[/tex]
Replace X With 5
[tex]3(5-4)+(2)(5)-5^2[/tex]
[tex]=-12[/tex]
I Hope This Helps
Please Mark Me As Brainliest :)
b) The height of the control tower. a) The shortest distance between the pilot and the base of the control tower. From a horizontal distance of 10.5km, a pilot observes that the angles of depression of the top and base of a control tower are 36° and 41 degrees respectively. Calculate he following:
From the calculations, the height of the tower is 26.4 Km
What is the angle of depression?If we know that the base of the tower is B and he top of the tower is T then to find the shortest distance between the pilot and the base of the control tower;
Sin 41 = 10.5//BP/
/BP/ = 10.5/Sin 41
/BP/ = 15.9 Km
Now, the height of the control tower is obtained from;
First /AB/ = √(15.9)^2 - (10.5)^2
/AB/ = 11.9 Km
Given that;
Tan 36 = 10.5//BT/
/BT/= 10.5/Tan 36
/BT/= 14.5 Km
Hence the height of the tower is 11.9 Km + 14.5 Km = 26.4 Km
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Consider the triangles.
Triangle P E C has angles 60 degrees, 58 degrees, blank. Triangle X W J has angles 58 degrees, 60 degrees, blank.
What can be concluded about these triangles?
Two pairs of corresponding angles are congruent, so the triangles are similar.
Two pairs of corresponding angles are congruent, so the triangles are congruent.
Angle J is congruent to angle P.
Angle C is congruent to angle W.
Two pairs of corresponding angles are congruent, so the triangles are similar.
The correct option is (A).
What is similarity in triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
As, the measurement of two angles are equal.
So, the angles are congruent.
Hence, by AA criteria the triangles are similar.
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Answer:
A
Step-by-step explanation:
Which graph represents the following system of inequalities?
y<-2x+4
yx<3
A graph which represents the given system of inequalities is Graph C.
What is an inequality?An inequality can be defined as a mathematical relation that compares two (2) or more integers and variables in an equation based on any of the following:
Less than (<).Greater than (>).Less than or equal to (≤).Greater than or equal to (≥).Based on the graph for the given system of inequalities (see attachment), we can infer and logically conclude that Graph C best represents them.
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what is 8.31752 to the correct 3 decimal places
Answer:
8.31752 to correct 3 decimal places =
Step-by-step explanation:
8.318
brainiest pls it helps
2(2x – 1) + 7 < 13 or –2x + 5≤-10
Answer:
x<2 or x ≥ 15/2
Step-by-step explanation:
Find x and y. please help ty!! :)
answer:
x=74 y=27
steps:
triangle in the middle is
180-126 = 54
180-85 = 95
180-149 = 31
126=2x+1+31
126=2x+32
2x=94
x=74
126+2y=180
2y=54
y=27
Solve the equation.
4.5=0.5n
