It is true that exponent laws apply all the time when simplifying variables
How to determine the true statement?The laws of exponent state that:
[tex](ab)^m = a^m * b^m[/tex]
[tex](a+ b)^m \ne a^m + b^m[/tex]
[tex](a- b)^m \ne a^m - b^m[/tex]
[tex](a/b)^m \ne a^m / b^m[/tex]
The above laws must be followed in all variables.
When any of the law is misinterpreted, misrepresented or misused in simplifying variables, the result would be incorrect
Hence, it is true that exponent laws apply all the time when simplifying variables
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Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 3 ≤ x ≤ 6.
Answer:
OC
1
2
ين
3
4
5
6
f(x)
69
64
59
54
49
44
Need Help
Answer:
this question is not clear i have read it twice an still dont understand it. Sorry
Question 1 of 15
Solve 18x+62 12x+18.
A. x ≥ 4
B. x≤ 4
C. x≤2
D. x ≥ 2
Answer:
18+62=80x
12+18=30x
x=80÷30=2
x>2
The first digit of a 2-digit number is randomly selected from the set {1, 2}. The second digit is
randomly selected from the set {1, 2, 3, 4}. What is the probability that the 2-digit number is
prime?
The probability that the 2-digit number is prime is 3/8
How to determine the probability?The sets are given as:
First digit = {1, 2}.
Second digit = {1, 2, 3, 4}
When the 2-digit is formed, we have:
Numbers = {11, 12, 13, 14, 21, 22, 23, 24}
In the above set, there are 3 prime numbers out of the 8 numbers.
Hence, the probability that the 2-digit number is prime is 3/8
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21. For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?
21. Line 1: Passes through (1, 7) and (5, 5)
Line 2: Passes through (−1, −3) and (1, 1)
Answer:
The given lines are perpendicular.
Step-by-step explanation:
In the question, two lines are given as line 1 passes through (1,7) and (5,5). Whereas, line 2 passes through (-1,-3) and (1,1).
It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.
To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel.
Step 1 of 2
Find the slope of first line.
[tex]$$\begin{aligned}m_{1} &=\frac{5-7}{5-1} \\m_{1} &=\frac{-2}{4} \\m_{1} &=-\frac{1}{2}\end{aligned}$$[/tex]
Step 2 of 2
Find the slope of first line.
[tex]$$\begin{aligned}&m_{2}=\frac{1-(-3)}{1-(-1)} \\&m_{2}=\frac{4}{2} \\&m_{2}=2\end{aligned}$$[/tex]
And
[tex]$$\begin{aligned}&m_{1} m_{2}=-\frac{1}{2}(2) \\&m_{1} m_{2}=-1\end{aligned}$$[/tex]
Since, both slopes are reciprocal of each other.
Therefore, the lines are perpendicular.
What is the approximate angle made by the stairway with the ground?
Answer: C
Step-by-step explanation:
[tex]\sin x=\frac{13}{18}\\\\x=\sin^{-1} \left(\frac{13}{18} \right) \approx \boxed{46.24^{\circ}}[/tex]
A rectangle is divided into two equal parts and a circle is divided into four parts and a circle is divided into four equal parts. One part of rectangle is shaded.
How many parts of the circle should be shaded so that both the figures have the same fraction shaded?(1 Point)
Answer:
2 parts
Step-by-step explanation:
The rectangle has a 1/2 ratio, because there are 4 parts of the circle, you will shade 2. This is because 2/4 ratio is simplified to 1/2.
What times itself gets 2230
There's no "whole" number that gets exactly to 2230 (but the question that you are asking is the square root of 2230 I believe) but the answer would essentially be about 47.22.
30. For the following exercises, given each set of information, find a linear equation satisfying the conditions, if possible.
30. f(-5) = -4, and f(5) = 2
Answer:
The required linear equation satisfying the given conditions f(-5)=-4 and f(5)=2 is
[tex]$$y=\frac{3}{5} x-1$$[/tex]
Step-by-step explanation:
It is given that f(-5)=-4 and f(5)=2. It is required to find out a linear equation satisfying the conditions f(-5)=-4 and f(5)=2. To find it out, first, represent the given conditions in the form of points and then find the slope of a line passing through these two given points. Then consider one of the points to give the linear equation of the line in the form [tex]$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$[/tex]
Step 1 of 4
Observe, f(-5)=-4 gives the point (5,-4)
And f(5)=2 gives the point (5,2)
This means that the function f(x) satisfies the points (-5,-4) and (5,2).
Step 2 of 4
Now find out the slope of a line passing through the points (-5,-4) and (5,2).
[tex]$$\begin{aligned}m &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\m &=\frac{2-(-4)}{5-(-5)} \\m &=\frac{2+4}{5+5} \\m &=\frac{6}{10} \\m &=\frac{3}{5}\end{aligned}$$[/tex]
Step 3 of 4
Now use the slope [tex]$m=\frac{3}{5}$[/tex] and use one of the two given points and write the equation in point-slope form:
[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$\\ $$(y-2)=\frac{3}{5}(x-5)$$[/tex]
Distribute [tex]$\frac{3}{5}$[/tex],
[tex]$$\begin{aligned}&y-2=\frac{3}{5} x-\frac{3}{5} \times 5 \\&y-2=\frac{3}{5} x-3\end{aligned}$$[/tex]
Step 4 of 4
This linear function can be written in the slope-intercept form by adding 2 on both sides, [tex]$y-2+2=\frac{3}{5} x-3+2$[/tex]
[tex]$$y=\frac{3}{5} x-1$$[/tex]
So, this is the required linear equation.
Please help ASAP!
Robin can clean 72 rooms in 6 days.
How many rooms can Robin clean in 9 days?
I'll give 20 points away.
Thaddeus models the number of hours of daylight in his town as
d(t) = 2sin(xt) + 12, where dis the number of daylight hours and tis the
time in months since january 1.
what are the least and greatest numbers of daylight hours over the course of
a year?
a. least: 10 hours; greatest: 14 hours
b. least: 6 hours; greatest: 12 hours
c. least: 2 hours; greatest: 12 hours
o d. least: 7 hours; greatest: 14 hours
submit
Option (A) : least: 10 hours; greatest: 14 hours
The function f(x) = sin x has all real numbers in its domain, but its range is
−1 ≤ sin x ≤ 1.
How to solve such range questions?
Such questions in which every term is in addition and its range is asked is simplest ones to solve if we know the range of each of term. This can be seen from this question
Given: d(t) = 2sin(xt) + 12
= −1 ≤ sin (xt) ≤ 1.
= −2≤ 2 sin (xt) ≤ 2.
= 10 ≤ 2sin (xt) + 12 ≤ 14
= 10 ≤d(t) ≤ 14
Thus least: 10 hours; greatest: 14 hours
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i need help asap
1: Write a function that represents this process:
Take a number, x.
Multiply it by 4.
Subtract 2 from the result.
Then find the inverse of this function. Does the inverse represent the reverse of the process above? Explain why or why not.
2:Show why, for linear functions, a vertical translation is equivalent to a horizontal translation. For a linear function, what horizontal translation is equivalent to a vertical translation of 3 units up?
3:Alex says that the function f(x) = (3x)2 represents a vertical stretch of the quadratic parent function by a factor of 3. Marta says that it represents a horizontal compression by a factor of . Decide whether one student is correct, both are correct, or neither is correct.
4:For an unknown parent function f(x), write a function g(x) that is:
vertically stretched by a factor of 2,
shifted up 5 units, and
shifted right 4 units.
Explain how your function accomplishes these transformations.
Original function involved multiplication by 4 and then subtraction of 2.
Inverse function involves addition of 2 and then division by 4.
So the inverse represents the reverse of the given process.
What is function?
A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
According to the function,
Let the function be represented by f(x).
Step 1- Multiplying the number x by 4 results in 4x.
Step 2 - Subtracting 2 from results give 4x - 2.
So the function becomes:
f(x) = 4x - 2
We will find the inverse function by Replacing f(x) by y, and isolate x on one side of the equation and find the inverse:
[tex]y=4x-2\\\\ < br/ > y+2=4x\\ < br/ > x =\frac{1}{4} (y+2)\\ < br/ > f^-^1(y) = \frac{1}{4} (y+2)\\ < br/ > f^-^1(x) = \frac{1}{4} (x+2)[/tex]
Here,
The inverse function represents the reverse process.
Here, Original function involved multiplication by 4 and then subtraction of 2.
Inverse function involves addition of 2 and then division by 4.
So the inverse represents the reverse of the given process.
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What is the L.C.M of 4,10
Answer:
The LCM is 20
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
What is the LCM of 4, 10
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
The lcm stands for the least common multiple.
Using our times tables, let's find the lcm of 4 and 10.
[tex]\bf{Which\;is\;20}[/tex]. 40 is indeed a common multiple of 4 and 10, but it's not the least common multiple. The lcm is 20.
We can also list some multiples of 4 and 10 and find the lcm.
4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40...
10: 10, 20, 30, 40, 50, 60...
As you can see, we end up with the same answer: the lcm of 4 and 10 is indeed 20.
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=Lcm=20}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic \not1 \theta l}}[/tex]
lorena lifeguards at a lap pool that is 25 yards long, 10 ards wide, and 2 yards deep. There is a drain around he entire top edge of the pool. Each winter, Lorena uts a cover over the top surface of the pool. 25 yd Cover 2 yd 10 yd Which statements are true about the poor? Check all that apply The drain is best measured using perimeter The volume of water in the pool is measured in square yards The area of the cover is 250 yo The length of the drain is the perimeter of the top of the pool and is 100 yd One edge of the pool measures 10 yd orena lifeguards at a lap pool that is 25 yards long , 10 ards wide , and 2 yards deep . There is a drain around he entire top edge of the pool . Each winter , Lorena uts a cover over the top surface of the pool . 25 yd Cover 2 yd 10 yd Which statements are true about the poor ? Check all that apply The drain is best measured using perimeter The volume of water in the pool is measured in square yards The area of the cover is 250 yo The length of the drain is the perimeter of the top of the pool and is 100 yd One edge of the pool measures 10 yd
The true statements about the pool are
The drain is best measured using perimeter The area of the cover is 250 square yardsOne edge of the pool measures 10 ydHow to determine true statements?The given parameters are:
Length = 25 yardsWidth = 10 yardsDepth = 2 yardsTo measure the drain, we simply calculate the perimeter of the edge of the pool.
This means that (a) is correct
When the volume is calculated, the unit is cubic yard or yd³.
This means that (b) is wrong
The area of the cover is:
Area = Length * Width
This gives
Area = 25 yards * 10 yards
Evaluate
Area = 250 square yards
This means that (c) is correct
The length of the drain is calculated as:
Perimeter = 2 *(Length + Width)
This gives
Perimeter = 2 * (25 + 10)
Evaluate
Perimeter = 70
This means that (d) is wrong
Lastly (e) is correct, because the width of pool is 10 yards
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Write the equation of the circle graphed below. (-5,-5)
Answer:
(x+5)² + (y+5)² = 18
Step-by-step explanation:
Since the outline of the circle intersects with the point (-8,2), you can substitute to find the equation of the circle in the form (x-h)² + (y-k)² = r². First the center of the circle is given in the form (h,k). So (-5, -5) → (x – (-5))² + (y – (-5))² = r² → (x + 5)² + (y + 5)² = r².
Then to find r², substitute the given point with x and y.
((-8) + 5)² + ((-2) + 5)² = r²
(-3)² + (3)² = r²
18 = r²
r² = 18.
Find the total surface area of this cylinder.
Give your answer to 1 decimal place.
20 cm
11 cm
SOMEONE PLS HELP MEEEE
The solutions to the quadratic equations are:
a) [tex]x = \frac{3 \pm \sqrt{19}}{5}[/tex]
b) x = -8, x = 5.
A quadratic function is given according to the following rule:
[tex]y = ax^2 + bx + c[/tex]
The solutions are:
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
[tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]
In which:
[tex]\Delta = b^2 - 4ac[/tex]
Item a:
The coefficients are a = 5, b = -6, c = -2, hence:
[tex]\Delta = (-6)^2 - 4(5)(-2) = 76[/tex][tex]x_1 = \frac{6 + \sqrt{76}}{10} = \frac{6 + 2\sqrt{19}}{10} = \frac{3 + \sqrt{19}}{5}[/tex][tex]x_2 = \frac{6 - \sqrt{76}}{10} = \frac{6 - 2\sqrt{19}}{10} = \frac{3 - \sqrt{19}}{5}[/tex]Item b:
The equation is:
x² + 3x = 40
x² + 3x - 40 = 0.
It can be simplified as follows:
(x - 5)(x + 8) = 0.
Hence the solutions are:
x - 5 = 0 -> x = 5.x + 8 = 0 -> x = -8.More can be learned about quadratic equations at https://brainly.com/question/24737967
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A trader sold a tv for sh .18000 making a 20percent loss.For how much was he supposed to sell it in order to make 20percent profit.
Answer:
The trader was supposed to cell the TV for sh. 27000 in order to make 20% profit
==============
Let the cost price is x.
We have:
x - 20% = 18000Solve it for x:
x - 0.2x = 180000.8x = 18000x = 18000/0.8x = 22500The cost is 22500, find selling price with 20% profit:
22500 + 20% = 22500 + 0.2*22500 = 22500*1.2 = 2700012. Which one is not a polynomial? a) 4x² + 2x - 1 b) y - 3/y b) y² + √5y + 1
pls help ASAP
Answer:
b is not a polynomial
Step-by-step explanation:
b is not a polynomial because in y-3/y the y in denomination means y to the power -1 when it is taken to numerator and if power is negative then it is not a polynomial
Each of 15 learners will give a one and a half minute speech in their mother tongue. how long will it take to give the speeches?
It will take approx. 22 minutes and 30 seconds for the speeches.
What is Division?It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.
Here, Time duration of each learner = 1 minutes 30 seconds
= 3/2 minutes.
Total number of learners = 15
Time taken by all the speech category = 15 X 3/2
= 45/2
= 22 minutes 30 seconds
Thus, It will take approx. 22 minutes and 30 seconds for the speeches.
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solve the following equation for q. 5q - 3p + 4 = 4q - 2
For each experiment, determine whether events A and B are independent or dependent.
For the given experiments there are following outcomes.
A) Independent
b) Dependent
C) Dependent
D) Dependent
E) Independent
Probability can be defined as the ration of favorable outcomes to the total number of events.
For A)
A coin is tossed and a dice is flip. Both the event are independent of each other.
For B)
Choosing of clips have same total number of events that why both the events are dependent to each other.
For C)
It also have same number of total samples cause both cherries and nuts contained chocolate belongs to the same box. That's why its also dependent.
For D)
It is also dependent because the total number of sample is same for both the marbles.
For E)
It is independent, because for every box that picked reduces the size of sample and probability of picking new box wont depends on previous box.
Thus, this is how events are dependent and independent
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The Womens' World Record Marathon time has improved by 34.82% from Dale Grieg's (UK) time of 3 hrs 27 mins 45s in 1964 to Paula Radcliffe's (UK) time in 2003. Find Paula Radcliffe's World Record time.
Using proportions, it is found that Paula Radcliffe's World Record time was of 2h 15 min 25s.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In seconds, Dale Grieg's time is of:
3 x 3600 + 27 x 60 + 45 = 12,465s.
The Womens' World Record Marathon time has improved by 34.82%, that is, it was reduced by 34.82%, which means that the time is 65.18% of what it was, hence Paula Radcliffe's time is seconds is given by:
P = 0.6518 x 12465 = 8,125s.
In hours, minutes and seconds, we have that:
8,125s = 2h 15 min 25s.
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Anyone know what to do to figure this out ? :1/2(27+6)10
[tex]\bf{\dfrac{1}{2}(27+6)10 }[/tex]
Add 27 and 6 to get 33.
[tex]\bf{\dfrac{1}{2}(33)(10) }[/tex]
Multiply 1/2 by 3 to get 33/2.
[tex]\bf{\dfrac{33}{2}(10) }[/tex]
Express 33/2 (10) as a single fraction.
[tex]\bf{\dfrac{(33)(10)}{2} }[/tex]
Multiply 33 and 10 to get 330.
[tex]\bf{\dfrac{330}{2} }[/tex]
Divide 330 by 2 to get 165.
[tex]\bf{165 \ \ \to \ \ \ Answer}[/tex]
{ Pisces04 }CAN ANYONE HELP ME WITH THIS QUESTION?
Answer:
try 4
Step-by-step explanation:
8x4= 32
32-7=25
During a local high school football game, the height h feet of a football after t seconds can be represented by the function h(t) = −16t2+ 58t + 2. Find h(2.5) and explain its meaning.
h(2.5) = 47, and this mean that the height of the football after 2.5 seconds is 47 feet, using the quadratic function h(t) = -16t² + 58t + 2.
In the question, we are given that during a local high school football game, the height of h feet of a football after t seconds can be represented by the quadratic function h(t) = -16t² + 58t + 2.
We are asked to find h(2.5) and explain its meaning.
To find h(2.5), we substitute t = 2.5, in the quadratic function h(t) = -16t² + 58t + 2.
Thus,
h(2.5) = - 16(2.5)² + 58(2.5) + 2,
or, h(2.5) = - 16(6.25) + 145 + 2,
or, h(2.5) = -100 + 147,
or, h(2.5) = 47.
Hence, h(2.5) = 47, and this mean that the height of the football after 2.5 seconds is 47 feet, using the quadratic function h(t) = -16t² + 58t + 2.
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find intervals when the graph is growing or increasing or constant
The function shown in the graph is increasing over the interval (-1, 0) and (1, ∞). It is decreasing over the interval (-∞, -1) and (0, 1). The function does not remain constant.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The function shown in the graph is increasing over the interval (-1, 0) and (1, ∞). It is decreasing over the interval (-∞, -1) and (0, 1). The function does not remain constant.
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A 26-feet board is cut into 3 lengths where the first length is x, the second piece is 3 feet less than twice the first and the third piece is 2 feet more than the second. Find the length of the shortest piece.
We now have three equations, so we can solve them.
Let's define the length of the 3 boards in terms of x:
F=x
S=2x-3
T=2
F+S+T =26
x+2x-3+2 =26
3x =26+1=27
x =27/3 = 9 feet for First section
2x-3 =18-3 = 16 feet = Second
2 = Third
9+16+2 = 27
27 is the length of the shortest piece.
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Identify the postulate if possible
Answer:
Below.
Step-by-step explanation:
It's the Alternate Angle Theorem.
The opposite sides of the quadrilateral are parallel.
jackie has been averaging 3 hits for every 10 times at bat. What is the probability that she will get eactly 2 hits in her net 5 times at bat?
Answer:
the chance is 1.5 out of 5
Geometry question confused
Answer:
my ans will be wrong also and right also 50%5$chances it is an opposite angle so it is in out manner so iys sum is 180 so we have to subbtract
Step-by-step explanation:
65०to 180०(180०-65०=115०) i think ans is 115०the missing angle measurement is 115०in my opinion