Answer:
g-1(x) = -x/3 - 6.
Step-by-step explanation:
Let g(x) = y = -3(x + 6)
y = -3x - 18
3x = - y - 18
x = -y/3 - 6
Now replace x by the inverse g-1(x) and y by x, so
g-1(x) = -x/3 - 6.
mary drove 495 miles in 9 hours at the same rate, how long would it take her to drive 385 miles?
9. Evaluate f(x) = -2х2 - 4 fоr x = 3.
o
О-22
o
etric
o
О-18
o
О-10
The value of function f (x) at x = 3 is,
⇒ f (3) = - 22
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
⇒ f (x) = - 2x² - 4
Now, Put x = 3 in above function we get;
⇒ f (x) = - 2x² - 4
Put x = 3;
⇒ f (3) = - 2 (3)² - 4
⇒ f (3) = - 2 x 9 - 4
⇒ f (3) = - 18 - 4
⇒ f (3) = - 22
Thus, The value of function f (x) at x = 3 is,
⇒ f (3) = - 22
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What percent is equivalent to StartFraction 1 Over 25 EndFraction? 4% 5% 20% 25%
Convert the fraction to a decimal:
1/25 = 0.04
Multiply by 100 to get the percent:
0.04 x 100 = 4%
The fraction of 1/25 is equivalent to the 4% option (A) 4 % is correct.
What is the percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
We have a fraction:
= 1/25
In decimal:
= 0.04
In percent:
= 0.04×100
= 4%
Thus, the fraction of 1/25 is equivalent to the 4% option (A) 4 % is correct.
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Please help
Evaluate the expression for n=2
4(n+1)=
Answer:
12
Step-by-step explanation:
4(2+1)
4*3
12
Answer:
substitute n in bigger equation with 2.
4(2+1)
4×3=12
2y =30 the answer is 15 correct? They do not give that answer as an option
Answer:
Yes it is 15
Step-by-step explanation:
30/2 =15
Answer:
Yes, you are right! The answer is 15! :)
Step-by-step explanation:
2y = 30
Divide by two to get y on it's own.
y = 15
What is the answer to |x-4|<13
Answer:
The solution is -9 < x < 17.Step-by-step explanation:
|x-4|<13.
The above equation means, whatever the actual value of x is, the value of (x - 4) must be greater than - 13 and less than 13.
Hence, -13 < x - 4 < 13 or, -9 < x < 17. The value of x will be in between -9 and 17. The value of x can not be -9 or 17.
I got the first two can you help me with the last one PLZ
3. The sequence 6, 18, 54, 162, … shows the number of pushups Kendall did each week, starting with her first week of exercising.
(a) Is this an arithmetic or geometric sequence?
(b) How can you find the next number in the sequence?
(c) Give the rule you would use to find the 20th week.
1. Geometric Sequence
2. [tex]a_n = a_{n-1} * 3[/tex]
3. [tex]a_n = 6 * (3)^{n-1}[/tex]
Step-by-step explanation:
Given sequence is:
6, 18, 54, 162,....
Here
[tex]a_1 =6\\a_2 = 18\\a_3 = 54[/tex]
(a) Is this an arithmetic or geometric sequence?
We can see that the difference between the terms is not same so it cannot be an arithmetic sequence.
We have to check for common ratio (ratio between consecutive terms of a sequence) denoted by r
[tex]r = \frac{a_2}{a_1} = \frac{18}{6}= 3\\r = \frac{a_3}{a_2} = \frac{54}{18} = 3[/tex]
As the common ratio is same, the given sequence is a geometric sequence.
(b) How can you find the next number in the sequence?
Recursive formulas are used to find the next number in sequence using previous term
Recursive formula for a geometric sequence is given by:
[tex]a_n = a_{n-1} * r[/tex]
In case of given sequence,
[tex]a_n = a_{n-1} * 3[/tex]
So to find the 5th term
[tex]a_5 = a_4*3\\a_5 = 162*3\\a_5 = 486[/tex]
(c) Give the rule you would use to find the 20th week.
In order to find the pushups for 20th week, explicit formul for sequence will be used.
The general form of explicit formula is given by:
[tex]a_n = a_1 * r^{n-1}[/tex]
Putting the values of a_1 and r
[tex]a_n = 6 * (3)^{n-1}[/tex]
Hence,
1. Geometric Sequence
2. [tex]a_n = a_{n-1} * 3[/tex]
3. [tex]a_n = 6 * (3)^{n-1}[/tex]
Keywords: Geometric sequence, common ratio
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Joe went to a market and bought 5 carrots for a total of $10.50. If each carrot cost the same amount, how many dollars did each carrot cost? Express your answer as a decimal to the nearest hundredth
Final answer:
Each carrot cost $2.10, found by dividing the total cost of $10.50 by the number of carrots, which is 5.
Explanation:
The student’s question relates to the basic concept of unit price in mathematics. Joe bought 5 carrots for a total of $10.50. To find out how much each carrot cost, we divide the total cost by the number of carrots.
Here’s the calculation step-by-step:
Determine the total cost of the carrots, which is $10.50.
Determine the number of carrots bought, which is 5 carrots.
Divide the total cost by the number of carrots: $10.50 / 5 = $2.10.
So, each carrot costs $2.10 when expressed as a decimal to the nearest hundredth.
What is 4x-8 equivalent to?
Answer:
4x - 8 = -(8 - 4x)
Step-by-step explanation:
Answer: -32
First you would have to multiply 4x8 which is 32 and then just add the dash before the 32.
An economy package of cups has 630 green cups. If the green cups are 30% of the total package, how many cups are in the package? 10 pts pls help
There are 2100 cups in the package.
Step-by-step explanation:
Given,
Number of green cups in package = 630
This represent 30% of the total package.
Let,
x represent the total number of cups in package.
30% of x = 630
[tex]\frac{30}{100}*x=630\\0.30x=630[/tex]
Dividing both sides by 0.30
[tex]\frac{0.30x}{0.30}=\frac{630}{0.30}\\x=2100[/tex]
There are 2100 cups in the package.
Keywords: percentage, division
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i give up i might have to pull an allnighter
Answer:
Yes, they are congruent
Step-by-step explanation:
Yes, they are congruent because all the side and angle lengths are congruent.
Answer:
Yes
Step-by-step explanation:
Will someone please help me?
Answer:
The number of viruses was 2 times greater than bacteria.
Step-by-step explanation:
The number of viruses was [tex]2*10^9[/tex], and the number of bacteria was [tex]1*10^9[/tex].
To find how many times was the virus number greater than the bacteria number, we just divide the virus number by bacteria number:
[tex]\frac{ virus\:number }{bacteria\:number} =\frac{2*10^9 }{1*10^9} = 2*\frac{10^9}{10^9} =2[/tex]
Viruses are 2 times greater.
Answer:
Viruses are 2 times of the bacteria.
Step-by-step explanation:
Given:
Number of viruses = [tex]2\times 10^9[/tex]
Number of bacteria = [tex]1\times 10^9[/tex]
We have to found how many times viruses are greater than the bacteria.
To find how many times,we can divide both the numbers to compare its values.
Lets
Numerator = Number of viruses
Denominator = Number of bacteria
Dividing both we have,
⇒ [tex]\frac{2\times 10^9}{1\times 10^9}[/tex]
⇒ [tex]2\times 10^(^9^-^9)[/tex] ...[tex]\frac{ab^x}{cb^y}=\frac{ab^x^-^y}{c}[/tex]
⇒ [tex]2\times 10^0[/tex] ...[tex]a^0=1[/tex]
⇒ [tex]2[/tex]
So the viruses are 2 times of the bacteria.
Sally found 58 seashells on the beach, she gave Jason some of her seashells. She has 28 left. How many seashells did she give to Jason?
Sally gave 30 shells to Jason
Solution:
Given that, Sally found 58 seashells on the beach, she gave Jason some of her seashells
She has 28 left
To find: Number of sea shells she gave to Jason
From given,
Total number of shells she found = 58
Remaining shells = 28
Therefore,
Number of sea shells she gave to Jason = Total number of shells she found - Remaining shells
Number of sea shells she gave to Jason = 58 - 28 = 30
Thus Sally gave 30 shells to Jason
MATH HELP PLS THANK U
Answer:
Step-by-step explanation:
(14)
Given :
y = [tex]\frac{1}{2}[/tex][tex](x-3)^{2}[/tex] - 6
comparing with the standard form :
y = a[tex](x-h)^{2}[/tex] + k
vertex = ( h , k )
Focus = (h , k+14a )
Directrix = y = k
comparing the equation and the standard form ;
Vertex = ( 3 , -6 )
Focus = ( 3 , -6+14{1/2} )
Focus = ( 3 , 1)
Directrix ⇒ y = -6
(19)
[tex]x^{2}[/tex] + [tex]4y^{2}[/tex] = 13 .............. equation 1
[tex]x^{2}[/tex] - [tex]4y^{2}[/tex] = 5 ..................... equation 2
add equation 1 and 2
2[tex]x^{2}[/tex] = 18
divide through by 2
[tex]x^{2}[/tex] = 9
x = ±3
substitute x = 3 into equation 1
[tex]3^{2}[/tex] + 4[tex]y^{2}[/tex] = 13
9 +4[tex]y^{2}[/tex] = 13
4[tex]y^{2}[/tex] = 13 - 9
4[tex]y^{2}[/tex] = 4
[tex]y^{2}[/tex] = 1
y = ±1
Therefore , the solution is ( 3 , 1 ) or (-3 , -1 )
Answer:
14) vertex: (3, -6); focus: (3, -5.5); directrix: y = -6.5
17) see below for a graph
19) (±3, ±1) — four points
20) see below for the work
Step-by-step explanation:
14) The vertex form of a quadratic equation can be written as ...
[tex]y=\dfrac{1}{4p}(x-h)^2+k[/tex]
This parabola will have its vertex at (h, k), its focus at (h, k+p), and its directrix at y=k-p.
The given equation is ...
y = 1/2(x -3)² -6
Comparing this to the form above, we see that ...
4p = 2, h = 3, k = -6
From this, we can find the value of p to be ...
p = 2/4 = 1/2 . . . . divide the above equation by 4
Now, we know the parameters of the parabola are ...
vertex = (h, k) = (3, -6)focus = (h, k+p) = (3, -6 +1/2) = (3, -5.5)directrix ⇒ y = k-p = -6 -1/2 = -6.5_____
17) The equation of the parabola is given as ...
y = 1/4(x -1)² +5
Comparing the given equation to the form shown in the above problem, we see that ...
4p = 4 ⇒ p = 1(h, k) = (1, 5)So the parameters of the parabola are ...
vertex = (1, 5)focus = (1, 5+1) = (1, 6)directrix ⇒ y = 5-1 = 4The graph is shown below.
_____
20) It is convenient to show the solution steps before showing the solution. Hence we show problem 20 (steps) before problem 19 (solution).
The given system of equations is ...
x² +4y² = 13x² -4y² = 5The two equations can be added to give ...
(x² +4y²) +(x² -4y²) = (13) +(5)
2x² = 18 . . . . . . eliminate parentheses, collect terms
x² = 9 . . . . . . . . divide by 2
x = ±3 . . . . . . . . take the square root
__
The second equation can be subtracted from the first to give ...
(x² +4y²) -(x² -4y²) = (13) -(5)
8y² = 8 . . . . . . . eliminate parentheses, collect terms
y² = 1 . . . . . . . . . divide by 8
y = ±1 . . . . . . . . . take the square root
_____
19) Based on the above, the four solutions to the given system of equations are ...
(3, 1), (3, -1), (-3, 1), (-3, -1)
__
A graph is shown in the second attachment.
What shows a fractional and decimal equivalent of 9/20
Answer:
0.45 45%
Step-by-step explanation:
What is the domain and range of the relation shown in the table?
x y
0 3
5 4
9 2
32 7
domain: {0, 5, 9, 32} range: {y|y∈R}
domain: {x|x∈R} range: {2,3,4,7}
domain: {0, 5, 9, 32} range: {2,3,4,7}
domain: {2,3,4,7} range: {0, 5, 9, 32}
Answer:
domain: {0, 5, 9, 32} range: {2,3,4,7}
Step-by-step explanation:
we know that
For a set of ordered pairs, the first elements of each ordered pair represents the domain of the function and second elements of each ordered pair represents the range of the function.
The domain of a function is the set of all possible values of x
The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.
In this problem we have
values of x ----> [tex]\{0,5,9,32\}[/tex]
values of y ----> [tex]\{2,3,4,7\}[/tex]
therefore
domain: {0, 5, 9, 32} range: {2,3,4,7}
RSM Question NEED HELP!!! A cyclist rides into the country at an average speed of 10 miles per hour. When his bicycle gets a flat tire, he walks it back at an average speed of 3 miles per hour. If he returns home 6 and a half hours after he starts, how far into the country does he go?
Let x = distance traveled (not round trip)
x/10 + x/3 = 6.5
13/30x = 6.5
x = 15 miles
answer: 15 miles
Answer:
15 miles
Step-by-step explanation:
Find out the how far into the country does he go.
To proof
Let us assume that the total diatance travelled into the country be x .
Formula
As given
A cyclist rides into the country at an average speed of 10 miles per hour. When his bicycle gets a flat tire,
he walks it back at an average speed of 3 miles per hour.
If he returns home 6 and a half hours after he starts i.e the total time including the bike time and walk time of the cyclist be 6.5 hours.
Than the equation becomes
L.C.M of (10,3) = 30
Than the equation becomes
3x +10x = 195
solving
13x = 195
x = 15 miles into the country
Hence proved
How many hours will it take to complete a 63-km bike ride if you go 20 km per
hour the whole time?
Answer: time = 3.15 hrs
Step-by-step explanation:
distance = 63km
speed = 20km/hr
time = ?
speed = distance / time
therefore :
time = distance / speed
time = 63/20
time = 3.15 hours
Answer: 3 for whole numbers, but if you want to be exact, 3 and 3/20 (three and three twentieths)
Step-by-step explanation:
20 times 3 is 60, and there is 3 left so you would make it a fraction since it won't divide into 20.
Liability insurance covers any damage you might do to the apartment building. Contents insurance covers all your belongings. Your landlord requires that you purchase Liability insurance, but he will pay 20% of the cost if you buy both Liability and Contents insurance. If you buy both at the same time the cost is $45 per month. What is the cost to you per month if you buy both and take advantage of the landlord's offer?
Answer:
I believe that it would just be 20% of the $45 which would mean that you would have to pay $36 a month.
Hope this is helpful!
The cost to you per month, after the landlord's contribution, is $36.
If you buy both Liability and Contents insurance, and take advantage of the landlord's offer to pay 20% of the cost, the cost to you per month can be calculated as follows:
Let's assume the cost of Liability insurance is represented by 'L' and the cost of Contents insurance is represented by 'C'.
According to the information given, if you buy both insurances at the same time, the cost is $45 per month.
This means: L + C = $45
The landlord is willing to pay 20% of the cost, which is equal to 20% of ($45). To calculate this amount:
20% of $45 = (20/100) x $45 = $9
So, the landlord will pay $9 towards the cost of both insurances.
Now, if you subtract the landlord's contribution from the total cost, you'll get the amount you have to pay:
(L + C) - $9 = $45 - $9 = $36
Therefore, the cost to you per month, after the landlord's contribution, is $36.
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What is the slope of f(x)=4/5x-8
Answer:
the slope is 4/5
Step-by-step explanation:
because i learn that
What is the sum of the measures of the interior angles of a hexagon?
Answer:
720°
Step-by-step explanation:
The sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
Here n = 6 ( number of sides of a hexagon ), thus
sum = 180° × 4 = 720°
The sum of the measures of the interior angles of a hexagon is [tex]720^{\circ}[/tex]
A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain. The bounded plane region, the bounding circuit, or the two together, may be called a polygon. A hexagon is a six-sided polygon or [tex]6-[/tex]gon. Interior angles are those that lie inside a polygon.
The total of the internal angles of any simple hexagon is [tex]\boldsymbol{720^{\circ}}[/tex]
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Which property is demonstrated in the equation 0×25=0 ?
Simplfy the expression 3x+4(x-6)-3(x-7)
Answer:
the answer is 4x-3
Step-by-step explanation:
To simplify the expression 3x + 4(x - 6) - 3(x - 7), distribute the multiplication across the parentheses, combine like terms, and simplify to get the final result: 4x - 3.
To simplify the expression 3x + 4(x - 6) - 3(x - 7), follow these steps:
Distribute the 4 into the second parenthesis: 4 imes x - 4 imes 6 which gives 4x - 24.
Distribute the -3 into the third parenthesis: -3 imes x + (-3) imes (-7) which gives -3x + 21.
Combine like terms with the rest of the expression: 3x + (4x - 24) + (-3x + 21).
Add/subtract the x terms and constant terms: 3x + 4x - 3x (which simplifies to 4x) and -24 + 21 (which simplifies to -3).
The simplified form of the expression is 4x - 3.
The sum of two numbers is 119. If 4 times the smaller number is subtracted from the larger number the result is nine. Find a two numbers.
The larger number is 97 and smaller number is 22.
Step-by-step explanation:
Let,
The two numbers are x and y.
According to given statement;
x+y=119 Eqn 1
y-4x=9 Eqn 2
Subtracting Eqn 2 from Eqn 1
[tex](x+y)-(y-4x)=119-9\\x+y-y+4x=110\\5x=110[/tex]
Dividing both sides by 5
[tex]\frac{5x}{5}=\frac{110}{5}\\x=22[/tex]
Putting x=22 in Eqn 1
[tex]22+y=119\\y=119-22\\y=97[/tex]
The larger number is 97 and smaller number is 22.
Keywords: linear equation, elimination method
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Please help with these 4 problems. See attachment
:
m +3m + 6 = 4m - 9+ 15
Solve for the variable
Answer:
Solution: each real numberStep-by-step explanation:
[tex]m+3m+6=4m-9+15\qquad\text{combine like terms}\\\\(m+3m)+6=4m+(-9+15)\\\\4m+6=4m+6\qquad\text{subtract}\ 4m\ \text{from both sides}\\\\4m-4m+6=4m-4m+6\\\\6=6\qquad\bold{TRUE}\\\\\bold{CONCLUSION:}\ \text{infinitely many solutions}[/tex]
What is the 60th term in this sequence?
-6, -3,0,3,...
Answer:
54.
Step-by-step explanation:
Start at 60 and subtract 6. That leaves you with 54.
The 60th term in the arithmetic sequence -6, -3, 0, 3, ... can be determined using the formula of an arithmetic sequence, which results in a value of 171.
An arithmetic sequence, also known as an , is a sequence of numbers in which each term is obtained by adding a fixed constant to the previous term. In simpler terms, it's a sequence where the difference between any two consecutive terms is always the same.
The given sequence is an arithmetic progression where each term differs from the previous term by a constant value. In this case, the common difference[tex](\(d\))[/tex]between consecutive terms is 3.
To find the 60th term of this sequence, we can use the formula for the nth term of an arithmetic sequence:
[tex]\[a_n = a_1 + (n - 1) \cdot d\][/tex]
Here,[tex]\(a_n\)[/tex]represents the nth term, \(a_1\) is the first term, \(n\) is the term number we want to find, and \(d\) is the common difference.
In this sequence:
- The first term [tex](\(a_1\)) is -6.[/tex]
- The common difference [tex](\(d\)) is 3.[/tex]
- We want to find the 60th term, so [tex]\(n = 60\).\\[/tex]
Now, we can substitute these values into the formula:
[tex]\[a_{60} = -6 + (60 - 1) \cdot 3\][/tex]
[tex]\[a_{60} = -6 + 59 \cdot 3\][/tex]
[tex]\[a_{60} = -6 + 177\][/tex]
[tex]\[a_{60} = 171\][/tex]
Therefore, the 60th term in this arithmetic sequence is 171. This means that if you continued the sequence, the 60th term would be 171 units greater than the first term (-6), following the pattern of adding 3 at each step.
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Choose the best answer.
Jim Tree sold 3 items for cash.
Where would Jim list the amount received?
-Equipment Assets
-Other Assets (includes -receivables)
-Cash Assets
-Owner's Equity
-Liabilities - Accounts -Payable
Answer:
Cash assets is the answer
A rectangular garage is 12 meters long and 10 meters wide. What is its perimeter?
What are the x- and y-intercepts of -6x+4y=96
Answer:
Step-by-step explanation:
to find the x intercept, sub in 0 for y and solve for x
-6x + 4y = 96
-6x + 4(0) = 96
-6x = 96
x = -96/6
x = -16.....ur x intercept is -16 or (-16,0) <===
to find the y intercept, sub in 0 for x and solve for y
-6x + 4y = 96
-6(0) + 4y = 96
4y = 96
y = 96/4
y = 24....so ur y int is 24 or (0,24) <===
[tex]\text{Find the x and y intercepts:}\\\\\text{x intercepts:}\\\\\text{Plug in 0 to y}\\\\-6x+4(0)=96\\\\\text{Solve:}\\\\-6x+4(0)=96\\\\-6x=96\\\\\text{Divide both sides by -6}\\\\\boxed{x=(-16,0)}\\\\\text{y intercept:}\\\\\text{Plug in 0 to x}\\\\-6(0)+4y=96[/tex]
[tex]\text{Solve:}\\\\-6(0)+4y=96\\\\4y=96\\\\\text{Divide both sides by 4}\\\\\boxed{y=(0,24)}[/tex]