What is the inverse of the function g(x)=-3(x + 6)?
Please help me ASAP
Answer:
Inverse g(x) = -x/3-6
Step-by-step explanation:
To understand this just think g(x) as y so
we got y= -3(x+6) after that we change the minus three to left
so we got -y/3 because -3 is multiply. After that plus 6 came and become minus 6.
After all,you have to replace x in y place.
y = -3(x +6)
-y/3 = x +6
-y/3 -6 = x
-x/3 -6 = g(x)
A car travels a distance of 210 m in a time of 6 seconds. Calculate the time in seconds for the car to travel a distance of 1928 m.
Answer:
It will take 55.08 seconds.
Step-by-step explanation:
6 seconds = 210m
1 second = (210÷6)
= 35m
1928m ÷ 35m
=55.08 seconds
Answer = it will take 55.08 seconds to travel 1928m
Question 9 of 10 Which of these groups of values plugged into the TVM Solver of a graphing calculator will return the same value for PV as the expression ($505)((1+0.004) - 1) ? (0.004)(1+0.004) Question 9 of 10 Which of these groups of values plugged into the TVM Solver of a graphing calculator will return the same value for PV as the expression ( $ 505 ) ( ( 1 + 0.004 ) - 1 ) ? ( 0.004 ) ( 1 + 0.004 )
The TVM solver is a tool found in graphing calculators, that solve Time Value of Money problems.
The group of values that will return the same value as the given expression is;
D. N = 24; I% = 3.6; PV =; PMT = -415; FV = 0; P/Y = 12; C/Y = 12; PMT :END
What is Present Value?
Present value (PV) formula finds application in finance to calculate the present day value of an amount that is received at a future date.
In the TVM solver, we have;
I = The annual percentage rate
N = n × t
t = The number of years
PV = Present value
PMT = Payment
P/Y = Number of payments per year = n
C/Y = Number of compounding periods per year = n
The formula for monthly payment is presented as follows;
[tex]P = \frac{M[(1+r/n)^{nt} - 1]}{(r/n)(1+r/n)^{nt}}[/tex]
M = [tex]\frac{P.(r/n)(1+ r/n)^{nt} }{(1+ r/n)^{nt} - 1}[/tex]
Therefore, we get;
Where;
M = PMT = -415
P = PV
r = I
P/Y = n = 12
Therefore;
0.003 = I/12
I = 0.003 X 12 = 3.6%
N = n X t = 24
The value of the equation is the present value, PV = ?
When payment are made based on the PV, we have FV = 0
The group of values the same value as the expression
P = [tex]\frac{(415)[(1+0.003)^{24}-1]}{(0.003)(1+0.003)^{24}}[/tex]
when plugged into the TVM solver of a calculator is;
D. N = 24; I% = 3.6; PV =; PMT = -415; FV = 0; P/Y = 12; C/Y = 12; PMT :END
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Find (f • g) (x) Assume x>0
Answer:
[tex]\textsf{B.} \quad (f \cdot g)(x)=10x[/tex]
Step-by-step explanation:
Given:
[tex]\begin{cases}f(x)=\sqrt{50x}\\g(x)=\sqrt{2x}\end{cases}[/tex]
[tex]\begin{aligned}\textsf{As }(f \cdot g)(x) & = f(x) \cdot g(x)\\\implies (f \cdot g)(x)& = \sqrt{50x} \cdot \sqrt{2x}\end{aligned}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}:[/tex]
[tex]\begin{aligned}\implies (f \cdot g)(x) &= \sqrt{50x2x}\\& = \sqrt{100x^2}\end{aligned}[/tex]
Rewrite 100 as 10²:
[tex]\implies (f \cdot g)(x)=\sqrt{10^2x^2}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^bc^b=(ac)^b:[/tex]
[tex]\implies (f \cdot g)(x)= \sqrt{(10x)^2}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]
[tex]\implies (f \cdot g)(x)=10x[/tex]
Mr wong predicted that he would sell 45 automobiles , he actually sold 48
Answer:
well done mr wong lol
Step-by-step explanation:
what's the question is it the percent he beat his prediction?
if it is then its 48 divided by 45 times 100
this equals 106.67%
then take this away from his prediction percent originally which is 100%
106.67-100= 6.67%
You can walk over the mountains to
your campsite or take a safer, easier trip around the mountains. You
are on the ground at P(0, 0) and the campsite is at C(-2, 7). You
travel around the mountain by going to A(2, 5). The coordinate
system is measured in meters. Draw a diagram of the situation.
Find PA and AC.
Answer:
PA = [tex]\sqrt{29}[/tex]
AC =[tex]\sqrt[2]{5}[/tex]
Step-by-step explanation:
distance formula : if [tex](x_{1},y_{1}) and (x_{2},y_{2})[/tex] are two points on a line segment then distance between both the points is given by distance formula.
[tex]d = \sqrt{[(x_{2} - x_{1} )^2 +(y_{2} - y_{1})^2]}[/tex]
therefore ,
given points are , A(2, 5), P(0, 0), C(-2, 7).
so PA = [tex]\sqrt{[({2} - {0} )^2 +({5} - {0})^2]} = \sqrt{({2} )^2 +({5} )^2}[/tex]
PA = [tex]\sqrt{\229}[/tex]
similarly,
AC = [tex]\sqrt{[({-2} - {2} )^2 +({7} - {5})^2]} = \sqrt{({4} )^2 +({2} )^2}[/tex]
AC = [tex]\sqrt{20} = \sqrt[2]{5}[/tex]
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answer?......................
Answer:
22
Step-by-step explanation:
6( n^2 +2)
-----------------
n
Let n = 3
6( 3^2 +2)
-----------------
3
Parentheses first
6( 9 +2)
-----------------
3
6( 11)
-----------------
3
Top of the fraction next
66
-----
3
Divide
22
2. The letters from the word MATH are placed in a hat. What is the probability that you select an A when you are choosing a letter without looking? A. What is asked in the problem? 8. What are the given numbers? What operation will you use? D What is the mathematical sentence? E What is the answer to the problem? V. A
The probability of getting M from the word MATH placed in hat is 0.25.
Probability is defined as the ratio of the number of favorable results to the total number of elements of an event.
P= number of favorable outcomes / total number of outcomes of an event
A. The problem is the probability of finding A
B. The given are MATH i.e. {M,A,T,H}
C. the operation used will be selecting a word from hat of word MATH
D. the mathematical statement from the probability of finding M will be
P(getting M from word MATH)
E. the answer to the problem will be calculated as
no. of element in the hat=4 i.e. {M,A,T,H}
no. of favorable outcomes= 1 i.e. {A}
P(getting A from word MATH) = number of favorable outcomes/ number of total outcomes
⇒ P(getting A from word MATH) = 1/4
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write the faction in the simplest form 28/36
Answer:
7/9
Step-by-step explanation:
Divide the numerator and denominator by 4.
28/36 = 7/9
Answer:
7/9
Step-by-step explanation:
28 and 36 are both divisible by 4.
28÷4 is 7 and
36÷4 is 9
28/36 = 7/9
Gerald purchased a rectangular plot of land. the length of the plot is 20 feet more than the width. the cost of the land was $12 per square foot. gerald also had a fence put around the entire perimeter of the plot, at a cost of s8 per linear foot. the total amount he spent on both the land and the fence was $10,560. part a write an equation in two variables for the perimeter, p, and an equation in two variables for the area, a, of the plot of land where x is the width of the plot in feet. provide evidence to support your equations
Answer:
P =2(x+ y) [tex]ft[/tex].
A =xy [tex]ft^{2}[/tex]
Step-by-step explanation:
perimeter of rectangle (P)= 2(L+B
Area of rectangle (A) = L×B
Given,
width = 'x'
length = y = x+20
therefore using above formula
P = 2(x+20 + x) = 2(2x+20)
A = (x+20)(x)
cost of land per square foot = $12
cost of land per linear foot = $8
total cost of land = $10560
now,
P×8 + A×12 = 10560
2(2x+20)×8 + (x+20)(x)×12 = 10560
32x + 320 + 12x²+ 240x = 10560
12x² + 272x = 10240
12x² + 272x - 10240 = 0
solving this quadratic equation using Discriminant method
x = [-b ±√(b² - 4ac)]/2
where b is the coefficient of x
a is the coefficient of x²
and c is the constant term
by replacing values in the above formula
x = 19.5 , x = -42.24
as the area cannot be negative therefore -42.24 is neglected
hence x = 19.5ft
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A. Yes, the points shown on the line would be part of y=0.5x
B. Yes, all proportions can be shown on a graph of this line
C. No, the points shown would not be part of y=0.5x
D. No, the proportions cannot be represented on a graph
Answer:
B
Step-by-step explanation:
given the graph of y = 0.5x
Then any point on the line satisfies y = 0.5x
consider the points given
x = 1 then y = 0.5 × 1 = 0.5 ⇒ (1, 0.5 ) is on the line
x = 4 then y = 0.5 × 4 = 2 ⇒ (4, 2 ) is on the line
Can yall help me Find m/1.
Answer:
mAngle1 = 33°
Step-by-step explanation:
The three angles in a triangle add up to 180°.
31° + 116° + x = 180°
147° + x = 180°
Subtract 147° from both sides.
x = 33°
The measure of Angle1 is 33°
perpendicular to the line y =6 - 3x; passes through (-3, -1)
Answer:
[tex]y=\frac{1}{3}x[/tex]
Step-by-step explanation:
Perpendicular lines
Perpendicular lines have slopes whose product is -1. In other words, to find a line that is perpendicular to a given line, the new line must have a that is the opposite reciprocal of the original line.
Passing through a point
Additionally, if a line contains a point, then the point must be a solution to the equation (meaning, when you plug in the "x" and "y", the equation must be true).
Finding our perpendicular line
Work on slope first
To find the slope of the original line, rewrite the original line in slope-intercept form: [tex]y=mx+b[/tex]
[tex]y=6-3x\\y=6+(-3x)\\y=(-3x)+6\\y=-3x+6\\y=-\frac{3}{1}x+6[/tex]
In this form, the slope is the number multiplied to the "x", so the original slope is -3/1.
Thus, the slope of the new perpendicular line will be the opposite reciprocal of -3/1 ... which is 1/3.
Writing what we do know about the new perpendicular line, we have [tex]y=\frac{1}{3}x+b[/tex]
Making sure it passes through the point
This new line is also supposed to contain the point (-3,-1), so (-3,-1) must be a solution to the equation, for whatever constant-value the "b" is. To find out the "b", substitute the known quantities, and solve:
[tex]-1=\frac{1}{3} (-3)+b\\-1=-1+b\\(-1)+1=(-1+b)+1\\0=b[/tex]
Substituting this into our equation:
[tex]y=\frac{1}{3}x+(0)\\y=\frac{1}{3}x[/tex]
Conclusion
So, the equation for a line that is perpendicular to the original line [tex]y=6-3x[/tex], and that also passes through (-3,-1) is [tex]y=\frac{1}{3}x[/tex]
2. The smallest number from the given numbers 6895, 4875 and 5689 will have its smallest digits at place. (A)
The smallest digit of the smallest number is at the thousands place.
What is Number System ?The system of representing numbers is called Number System.
The given numbers are 6895 , 4875 , 5689
The smallest number among these is 4875
The smallest digit in this number is 4
4 is at thousands place
Therefore , The smallest digit of the smallest number is at the thousands place.
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what is
f(-1)=-3x^{2}+7x+4
Step-by-step explanation:
please mark me as brainlest
Genesis is going to see a movie and is taking her 3 kids. Each movie ticket costs $15 and there are an assortment of snacks available to purchase for $3 each. How much total money would Genesis have to pay for her family if she were to buy 6 snacks for everybody to share? How much would Genesis have to pay if she bought x snacks for everybody to share?
Total cost with 6 snacks:
Total cost with x snacks:.
need answer quickly as possibly!
Answer #1:
The total cost with 6 snacks is $78.
Answer #2:
The total cost with x snacks is represented by the expression 60 + 3x.
Step-by-step explanation for answer #1:
Starting off with what we know:
Genesis has 3 kids, so there are 4 people total including Genesis.Each movie ticket is $15.Each snack is $3.To answer the question of how much money Genesis would have to pay for her family if she bought 6 snacks for everybody, first consider the total cost of the movie tickets.
Multiply the total number of people by the cost of each movie ticket:
[tex]4* 15=60[/tex]
Genesis will be paying $60 total only to see the movie with her 3 kids. To find the total cost of both seeing the movie and buying 6 snacks, simply multiply the number of snacks by the cost of each snack:
[tex]6 * 3=18[/tex]
Then, add the total cost of the movie tickets by the total cost of the snacks to achieve your first answer:
[tex]60+18=78[/tex]
The total cost with 6 snacks is $78.
Step-by-step explanation for answer #2:
To find the total cost of "x" snacks (x is being used as a variable term to represent a quantity subject to change), we can create an algebraic expression.
Let "t" represent the total cost.
Since we've established that finding the total cost is just a matter of adding the total cost of movie tickets (60) and the total cost of snacks (3 multiplied by the number of snacks), let "x" represent the number of snacks in the equation to find the total cost with x snacks:
[tex]60+3x=t[/tex]
The total cost with x snacks is represented by the expression 60 + 3x.
Based on the given data, the total cost of 6 snacks: $78. total cost with x snacks: $60 + (3x).
Use the concept of multiplication defined as:
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that,
Genesis is going to see a movie with her 3 kids.
Each movie ticket costs $15.
There are snacks available for purchase at $3 each.
Genesis wants to buy 6 snacks for everybody to share.
To calculate the total cost for Genesis and her 3 kids,
Consider the movie tickets and the snacks.
The cost of the movie tickets can be calculated by multiplying the number of people (4 in this case) by the cost of each ticket ($15).
So, Genesis would have to pay 4 x $15 = $60 for the movie tickets.
Now, let's calculate the total cost if Genesis were to buy 6 snacks for everybody to share.
Each snack costs $3, so 6 snacks would cost 6 x $3 = $18.
Therefore, the total cost for Genesis would be,
$60 (movie tickets) + $18 (snacks) = $78.
If we consider x snacks for everybody to share,
The total cost for snacks would be x $3.
So, the final cost would be $60 (movie tickets) + (3x) (snacks).
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When you eat certain foods, sugar is immediately released into your bloodstream. many doctors say kids should only take in 6 teaspoons (24 grams) of added sugar each day. jack is making lemonade for his school and wants to follow that recommendation. he wants to make 206 servings, following the recommendation, how many grams of sugar will he use?
Answer:
4,944
Step-by-step explanation:
The steps to simplify the expression -100 ÷ 3 x (-0.6) are shown.
Answer:
That is the answer for you step 2
The length of a rectangle is 7 inches and the width is 42 inches. What is the ratio,
using whole numbers, of the length to the width?
Answer:
6 : 1
Step-by-step explanation:
The length is the longer side compared to the width.
Hence, the length is 42 inches and width is 7 inches.
Taking the ratio :
Length : Width42 : 77 x 6 : 76 : 1Answer:
1 : 6
Step-by-step explanation:
42 /7 = 6
We will have to simply the ratios in order to get the answer.
Maël mixes 15 milliliters (mL) of bleach with 3.75 liters (L) of water to make a sanitizing solution for a daycare. The amounts of bleach and water always have to be proportional when he makes sanitizing solution. Which of the following could be combinations of volumes of bleach and water for Maël's sanitizing solution?
A. 12 mL bleach and 3 L water
B. 6 mL bleach and 1.5 L water
C. 3 mL bleach and 0.75 L water
D. 20 mL bleach and 5.5 L water
E. 11 mL bleach and 3.75 L water
Answer: A,B,C
Step-by-step explanation: A,B,C is the answer
The graph of the function f(x) = –(x + 3)(x – 1) is shown below.
On a coordinate plane, a parabola opens down. It goes through (negative 3, 0), has a vertex at (negative 1, 4), and goes through (1, 0).
Which statement about the function is true?
The function is positive for all real values of x where
x < –1.
The function is negative for all real values of x where
x < –3 and where x > 1.
The function is positive for all real values of x where
x > 0.
The function is negative for all real values of x where
x < –3 or x > –1.
Answer:
The second statement is true.
Step-by-step explanation:
Draw the corresponding parabola and use it to verify all statements.
Answer:
The function is negative for all real values of x where
x < –3 and where x > 1.
Step-by-step explanation:
The answer above is correct.
The top of a tree makes angles s and t with points K and L on the ground, respectively, such that the angles are complementary. Point K is x meters and point L is y meters from the base of the tree.
1. In terms of x and y, find the height of the tree. Include your calculations.
2. If m∠t = 40° and y = 8 meters, calculate the height of the tree, rounded to two decimal places.
1. In terms of x and y, the height of the tree is [tex]h = y \times tan \ t^\circ[/tex] and[tex]h = x \times tan \ s^\circ[/tex]
2. The height of the tree is 6.71 meters
Trigonometry
From the question, we are to determine the height of the tree in terms of x and y
Using SOH CAH TOA, we can write that
[tex]tan \ t^\circ =\frac{h}{y}[/tex]
∴ [tex]h = y \times tan \ t^\circ[/tex]
Also,
[tex]tan \ s^\circ =\frac{h}{x}[/tex]
∴ [tex]h = x \times tan \ s^\circ[/tex]
2. If m∠t = 40° and y = 8 meters,
Then, the height of the tree
h = 8 × tan40°
h = 6.71 meters
Hence, the height of the tree is 6.71 meters
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In the triangle above, what is the measure of
A.
M
B.
M
C.
M
D
, cannot be determined
Could someone explain why the value of x is (-2).
Answer:
x = -2
Step-by-step explanation:
2x^3 +16 = 0
We are solving for x
Subtract 16 from each side
2x^3 +16- 16 = 0-16
2x^3 = -16
Divide each side by 2
(2x^3 ) /2 = -16/2
x^3 = -8
Take the cube root of each side
[tex]\sqrt[3]{x^3} = \sqrt[3]{-8}[/tex]
x = -2
Answer:
[tex]x=-2[/tex]
Step-by-step explanation:
Given equation:
[tex]2x^3+16=0[/tex]
To solve for the unknown variable x, apply arithmetic operations to isolate the variable.
Subtract 16 from both sides:
[tex]\implies 2x^3+16-16=0-16[/tex]
[tex]\implies 2x^3=-16[/tex]
Divide both sides by 2:
[tex]\implies \dfrac{2x^3}{2}=\dfrac{-16}{2}[/tex]
[tex]\implies x^3=-8[/tex]
Take the cube root of both sides:
[tex]\implies \sqrt[3]{x^3}=\sqrt[3]{-8}[/tex]
[tex]\implies x=-2[/tex]
When taking the cube root of a negative number, the result will be negative. To understand why, examine what happens when we cube a negative number.
When a number is cubed, it is multiplied by itself, then by itself again.
When multiplying a negative number by another negative number, the result is always positive.
When multiplying a positive number by a negative number, the result is always negative.
Therefore:
[tex]\begin{aligned}\implies (-2)^3 &= -2 \cdot -2 \cdot -2\\ & = 4 \cdot -2\\& = -8\end{aligned}[/tex]
So if -8 is cube rooted, the result is -2.
Solve for x.
log x = 3
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{x = 1000}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{log(x) = 3}[/tex]
Find: [tex]\textsf{The value of x}[/tex]
Solution: In order to solve for x we need to get rid of the log which means that we need to put it to the power of the same number as the base. When a base isn't displayed it defaults to 10 so we raise everything to the base of 10.
Get rid of log
[tex]10^{\textsf{log}_{10}\textsf{(x)}}} = 10^{\textsf{3}}[/tex][tex]x = 10^{\textsf{3}}[/tex][tex]x = 1000[/tex]Therefore, the final answer would be that x is equal to 1000.
What expression below is equivalent to -71n -
29?
A) -29 - 71n
B) 71n + (-29)
C) 29 + 71n
D) -29 - (-71n)
Answer:
A
Step-by-step explanation:
both numbers are negative, you can rearrange them in any order provided you keep the sign
Reason:
An expression in the form -a-b is the same as -a + (-b)
Recall we can add two numbers in any order we want. For instance, 2+3 = 3+2 since both sides are equal to 5. This is the commutative property of addition.
Therefore, the -a + (-b) is the same as -b + (-a) which in turn becomes -b - a
In short: -a - b = -b - a
This rule lets us say that -71n - 29 = -29 - 71n
Is in between 2 number on the number line
Answer:
3 and 4
Step-by-step explanation:
well you can approximate by squaring values
2^2 = 4
3^2 = 9
4^2 = 16
the value should fall somewhere between 3 and 4 since the square root of 9 is 3 and the square root of 16 is 4
\In a mouse population, some mice have thicker fur than others, but there are more mice with thinner fur. The climate in which these mice live has slowly gotten colder.
How will this change in the environment most likely affect the mouse population?
The adaptation of thinner fur will be selected over thicker fur, and the population will remain unchanged.
The adaptation of thicker fur will be selected over thinner fur, and the population will remain unchanged.
The adaptation of thinner fur will be selected over thicker fur, and the population will evolve.
The adaptation of thicker fur will be selected over thinner fur, and the population will evolve.
The adjustment of thicker fur will be selected over thinner fur, and the population will develop. Then the correct option is D.
What is decision-making?Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.
In a mouse population, some mice have thicker fur than others, but there are more mice with thinner fur.
The climate in which these mice live has slowly gotten colder.
The change in the environment most likely affect the mouse population will be
The adjustment of thicker fur will be selected over thinner fur, and the population will develop.
Then the correct option is D.
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simplify (3+√5)(3+√2)
When we simplify (3 + √5)(3 + √2), the result obtained is:
9 + 3√2 + 3√5 + √10
Surd operationa√b × c√d = (a × c)√(b × d)
How to simplify (3 + √5)(3 + √2)(3 + √5)(3 + √2)
Expand by clearing the bracket
3(3 + √2) + √5(3 + √2)
9 + 3√2 + 3√5 + √10
Thus,
(3 + √5)(3 + √2) = 9 + 3√2 + 3√5 + √10
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Which of the following are solutions to the equation below?
Check all that apply.
(3x - 5)^2 = 19
Answer:
To solve the answer, you can do it in 2 ways:
1) you could take the square root on both sides and solve for x
OR
2)you could multiply 3x-5 times itself and subtract 19 on both sides and use the grouping or quadratic formula method to find x.
Hope it helps.
