Answer:
f of x equals 7 times one eighth to the x power
Step-by-step explanation:
Given phrase,
function f of x equals 7 times one half to the 3 times x power,
[tex]\implies f(x) = 7(\frac{1}{2})^{3x}[/tex]
By the power to power property of exponent,
That is,
[tex](a^m)^n=a^{m.n}[/tex]
[tex]f(x) = 7((\frac{1}{2})^3)^x[/tex]
[tex]f(x) = 7(\frac{1}{8})^x[/tex]
= f of x equals 7 times one eighth to the x power
A coordinate plane with a line passing through (negative 4, 3), (0, 1), and (4, negative 1). Which linear function is represented by the graph? f(x) = –2x + 1 f(x) = –f(x) equals negative StartFraction one-half EndFraction x plus 1.x + 1 f(x) = f(x) equals StartFraction one-half EndFraction x plus 1.x + 1 f(x) = 2x + 1
Answer:
Step-by-step explanation:
If these 3 points are collinear, then we can find the slope of the linear function using any 2 of those points. Suppose we use (-4, 3) and (0, 1):
As we move from (-4, 3) to (0, 1), x increases by 4 and y decreases by 2. Hence, the slope of this lilne is m = rise/run = -2/4, or m = -1/2.
Using the slope-intercept formula y = mx + b and replacing y with 1, x with 0 and m with -1/2, we get:
1 = (-1/2)(0) + b, or b = 1. Then the desired equation is y = f(x) = (-1/2)x + 1
Answer:
B
Step-by-step explanation:
293,671 in word from
Answer: two hundred ninety three thousand six hundred seventy one
To convert 293,671 into words, divide it into the thousands and ones part - resulting in 'two hundred ninety-three thousand, six hundred seventy-one'.
Explanation:Turning a number like 293,671 into words is a simple task once you understand the place value system used in English for numbers. This process involves breaking the number down into manageable chunks and then converting each chunk into words based on their respective values.
Firstly, we recognize that 293,671 falls in the 'thousands' range, as it's more than 1,000 but less than 1 million. Therefore, we divide the number into the 'thousands' part (293) and the 'ones' part (671).
The number 293 in words is 'two hundred ninety-three', and 671 is 'six hundred seventy-one'. Combining these with the appropriate place value gives us 'two hundred ninety-three thousand, six hundred seventy-one'.
How many inches are in 3 miles
Answer:
190,080 inches
Step-by-step explanation:
Inches converted into miles. 3 miles will equal to 190080 inches according to the conversion.
Hope this helped!
Nate
Is -34 a whole number, integer, rational number?
-34 is indeed a "whole number, integer, and a rational number." Whole numbers are full numbers including negatives, not including fractions, decimals, and percents. Integers are whole numbers can be negative or positive. Also rational numbers are anything that can be expressed as a fraction.
Hope this helps.
PLEASE HELP! (picture is shown)
which of the following points are collinear in this image?
Answer:
F, K & G
Step-by-step explanation:
Points are colinear if they lie on the same straight line.
only K , F & G line on a straight line.
The following points which are collinear in the image is Option (A) F,K and G.
What are collinear points ?Three or more points are said to be collinear if they lie on a single straight line. A line on which points lie, especially if it is related to a geometric figure is called an axis. Two points are always collinear since two points determine a line.
How to identify the collinear points in the figure ?From the definition of collinear points, we have to identify the points which are in a single straight line.
Apart from the rest other options, Option (A) signifies the points F,K and G which are on the single straight line of the vertex FG in the cube.
Therefore, the following points which are collinear in the image is Option (A) F,K and G.
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help pls pls pls pls pls
Answer:
12.I know that whole numbers go inside the integers circle, and that natural numbers (counting numbers) go inside the whole numbers circle. The irrational numbers circle is in its own category.]
13. It is true that 5 to the 2nd power is 25. So I guess you should just prove that it is true? The way they phrased the question was awkward.
Please mark brainliest! I would really appreciate it! :)
Jackie has 1/3 of a Hershey bar.steven has 4/12 of a Hershey bar.How much do they have together?
Answer: 2/3
Step-by-step explanation: To find how much of the candy bar they each have, we will have to add the fractions. To add unlike fractions such as 1/3 and 4/12, we first need to find a common denominator. The common denominator of 3 and 12 is simply the least common multiple of 3 and 12 which is 12. To get 12 in the denominator of 1/3, we multiply the numerator and denominator by 4 to get 4/12. Notice that our second fraction already has 12 in the denominator so we can now add these fractions.
[tex]\frac{4}{12}[/tex] + [tex]\frac{4}{12}[/tex] = [tex]\frac{8}{12}[/tex].
Notice that 8/12 can be reduced by dividing both the numerator and denominator by 4.
8 ÷ 4 = 2
12 ÷ 4 = 3
Therefore, Jackie and Steven have 2/3 of a Hershey bar.
Is V72 rational or irrational? Explain.
A number is rational if it is the result of a fraction.
Take any number, if you can write it down as a fraction, then that number is rational.
Example: 2,5 is rational because it's 5/2.
A number is irrational if it's real and IS NOT rational.
Example: pi is irrational, e is irrational and also
[tex] \sqrt{72} [/tex]
A detailed explanation of whether [tex]\sqrt{72}[/tex] is rational or irrational, with examples and definitions to support the answer.
To determine whether [tex]\sqrt{72}[/tex] is rational or irrational, let's first simplify the expression:
[tex]\sqrt{72}[/tex] = [tex]\sqrt{36*2}[/tex]
[tex]\sqrt{72} = \sqrt{36}[/tex] × [tex]\sqrt{2}[/tex]
[tex]\sqrt{72[/tex] = [tex]6\sqrt{2}[/tex]
Now, 2 is an irrational number, as it cannot be expressed as a fraction of two integers where the denominator is not zero. Since [tex]\sqrt{2}[/tex] is irrational and [tex]\sqrt{6}[/tex] is rational, the product [tex]6\sqrt{2}[/tex] is also irrational.
Therefore, [tex]\sqrt{72}[/tex] is irrational.
perfect square of 401
A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 401 is about 20.025. Thus, the square root of 401 is not an integer, and therefore 401 is not a square number.
Answer:
apparently In what I believe, 401 is not a perfect square mate!
Step-by-step explanation:
401 is an odd number, because it is not evenly divisible by 2.
A number is a perfect square (or a square number) if its square root is an integer; that is to say, it is the product of an integer with itself. Here, the square root of 401 is about 20.025.
Thus, the square root of 401 is not an integer, and therefore 401 is not a square number.
10) At 9:00 there are exactly 10 bacteria in a dish, and the population doubles every 15 minutes . Pick a time after 10:30 but before 12:00 and determine the number of bacteria in the dish at that time. Show all work supporting your answer.
Step-by-step explanation:
10 x 2 = 20 (after 15 minutes) 9:15
20 x 2 = 40 (after 30 minutes)
40 x 2 = 80 (after 45 minutes)
80 x 2 = 160 (after 60 minutes) - 10:00
160 x 2 = 320 (after 75 minutes)
320 x 2 = 640 (after 90 minutes)
640 x 2 = 1280 (after 105 minutes) - 10:40
There will be 1280 bacteria in the dish at 10:40.
what is the probability of rolling an odd number on one roll of dice
Answer: 1/2 or 50%
Step-by-step explanation: To find out what is the probability of rolling an odd number on a dice, we first need to understand what probability is. Probability is the likelihood that an event will happen. We can find the probability of an event using a ratio. Notice that in this problem, we are asked to find the probability of spinning an odd number. This means that the odd numbers will be a favorable outcome.
Image is provided.
If x+y+z=13 what is the value of (x-1)+(y+1)+(z-1)
Answer:
12
Step-by-step explanation:
(x-1)+(y+1)+(z-1)
= x -1 + y + 1 + z - 1
= x + y + z -1
= (x + y + z) -1
given that x+y+z = 13, substitute this value into the equation aove
(x + y + z) -1
= 13 - 1
= 12
What’s the slope of the line in the graph?
Check the picture below, let's use those two points on the line to get its slope.
[tex]\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{3}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{3}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{0}}}\implies \cfrac{2}{2}\implies 1[/tex]
Find the first, fourth, and 10th terms of the arithmetic sequence described by the given rule.
A(n) = -6 + (n - 1)(1/5)
[tex]\bf \begin{array}{ll} \stackrel{term}{n}&\stackrel{-6+(n-1)\frac{1}{5}}{value}\\ \cline{1-2} 1&-6+(1-1)\frac{1}{5}\\ &-6+0\\[1em] &-6\\[1em] 4&-6+(4-1)\frac{1}{5}\\ &-6+\frac{3}{5}\\[1em] &\frac{-27}{5}\\[1em] 10&-6+(10-1)\frac{1}{5}\\ &-6+\frac{9}{5}\\[1em] &\frac{-21}{5} \end{array}[/tex]
Answer with Step-by-step explanation:
We are given a arithmetic sequence as:
[tex]A(n)=-6+(n-1)(\dfrac{1}{5})[/tex]
We have to find the first, fourth and tenth term
First term:
n=1
[tex]A(1)=-6+(1-1)(\dfrac{1}{5})[/tex]
A(1)= -6
Fourth term:
n=4
[tex]A(4)=-6+(4-1)(\dfrac{1}{5})[/tex]
[tex]A(4)=-6+\dfrac{3}{5}[/tex]
[tex]A(4)=-\dfrac{27}{5}[/tex]
Tenth term:
n=10
[tex]A(10)=-6+(10-1)(\dfrac{1}{5})[/tex]
[tex]A(10)=-6+\dfrac{9}{5}[/tex]
[tex]A(10)=-\dfrac{21}{5}[/tex]
-4 1/3 + 5 2/3
step by step
Answer:
1 1/3
Step-by-step explanation:
-4 1/3 + 5 2/3 = -13/3 + 17/3 { change into improper form}
= { (-13) + 17 } / 3
= 4 / 3
= 1 1/3
what is the equation for the line of reflection?
Answer:
x=0
Step-by-step explanation:
92.3-(3.2 divided by 0.4) times 8
Answer:
28.3 that's the answer
Step-by-step explanation:
simplify 5^(-2)
PLEASE HURRY
Answer:
.04
i think
hope that helps
Answer: The required simplified value is 0.04.
Step-by-step explanation: We are given to simplify the following :
[tex]E=5^{-2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We will be using the following property of exponents :
[tex]a^{-n}=\dfrac{1}{a^n}.[/tex]
The simplify of (i) is as follows :
[tex]E\\\\=5^{-2}\\\\=\dfrac{1}{5^2}\\\\=\dfrac{1}{25}\\\\=0.04.[/tex]
Thus, the required simplified value is 0.04.
How would the sum of cubes formula be used to factor x^3y^3+343? Do not write the factorization
Answer:
[tex]\large\boxed{x^3y^3+343=(xy+7)(x^2y^2-7xy+49)}[/tex]
Step-by-step explanation:
[tex]x^3y^3=(xy)^3\\\\343=7^3\\\\x^3y^3+343=(xy)^3+7^3\qquad\text{use}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(xy+7)\bigg((xy)^2-(xy)(7)+7^2\bigg)=(xy+7)(x^2y^2-7xy+49)[/tex]
The cost of Mr. Patten’s car insurance increased by 5% to $86.82 per month. What was the cost of his insurance before it increased?
Answer:
Considering is a compunded increase rate of the yearly car insurance fee and x is the initial value of the insurance fee then
x×(1.05)^12=$86.82
×=$86.82/(1.05)^12
The cost of his insurance before it increased is $82.48.
Here,
The cost of Mr. Patten’s car insurance increased by 5% to $86.82 per month.
We have to find the cost of his insurance before it increased.
What is Percentage?
A percentage (from Latin per centum "by a hundred") is a number or ratio expressed as a fraction of 100.
Now,
The cost of Mr. Patten’s car insurance increased by 5% to $86.82 per month.
Increased cost = [tex]\frac{5}{100} * 86.82 = 4.34[/tex]
Hence, The cost of his insurance before it increased = $86.82 - $4.34
= $82.48
So, The cost of his insurance before it increased is $82.48.
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Describe how to find the sums -4+2 and -4+(-2) on a number line.
For -4+2, plot -4, then move to the right 2 spaces. You should land on -2.
For -4+(-2), plot -4 then move the left 2 spaces. You should land on -6.
Answer: Make a number line. Start at 0. For -4+2 you go back 4 on a number line. Then you add 2. You will end up on -2. For -4+(-2) you start at 0. You go back 4 until you reach -4, then you go back another 2. You should end up on -6.
The length of a rectangle is twice its width. The perimeter of the rectangle is 135 feet. Write an equation for this description.
Answer:
First of all, you should know that perimeter means, the sum of all the sides in the figure. So, if you have a lenght that is twice its widht, the ecuation must be, 6 width = 135 ft.
Step-by-step explanation:
Answer:
Step-by-step explanation:
twice means 2 , so you have to multiply 135 by 2 and there is your answer.
Laura has a backyard that she wants to renovate. Her
backyard is (x + 4) feet wide and (x + 6) feet long.
Laura wants to place a rectangular garden that is x
feet wide and (x + 2) feet long in the middle of her
backyard. Laura also wants to pour in concrete that
surrounds her garden in the backyard that will serve
as a walkway. What is the expression that represents
the area of the walkway? Refer to the diagram.
Answer:
Area of the walkway = 8x + 24
Step-by-step explanation:
Area of the total backyard = [tex]l\times b[/tex]
Area of total backyard = [tex](x+6)\times (x+4) = x^{2} +10x + 24[/tex]
Now, Area of the rectangular garden = [tex]l\times b[/tex]
Area of the rectangular garden = [tex]x (x+2) = x^{2} + 2x[/tex]
Now area of the walkway poured with concrete = Area of the backyard - Area of the rectangular garden
= [tex](x^{2} +10x +24) - (x^{2} +2x)[/tex]
= [tex]x^{2} + 10x +24 - x^{2} -2x[/tex]
= 8x + 24
Multiply: (3x + 2)(4x + 2)
Answer:
[tex]12x^{2} +14x+4[/tex]
Step-by-step explanation:
3x *4x = [tex]12x^{2}[/tex]
[tex]3x+4x*2=14x[/tex]
2 + 2 = 4
[tex]12x^{2} +14x+4[/tex]
If the ratio of m to n is 7 to 6, which of the following could be true?
O A. m = 8, n = 7
O B. m = 12,n= 14
O c.m=14, n=0
OD. m = 42, n = 42
O E. m = 7/3, n = 2
Answer:
E
Step-by-step explanation:
Consider each of the given values for m and n
A
m : n = 8 : 7 ≠ 7 : 6
B
m : n = 12 : 14 = 6 : 7 ≠ 7 : 6
C
m : n = 14 : 0 ≠ 7 : 6
D
m : n = 42 : 42 = 1 : 1 ≠ 7 : 6
E
m : n = [tex]\frac{7}{3}[/tex] : 2 = [tex]\frac{7}{3}[/tex] : [tex]\frac{6}{3}[/tex] = 7 : 6
Thus E is the only true ratio
Answer:
E. m = 7/3, n = 2
Step-by-step explanation:
The correct answer
Order the numbers from smallest to largest: 1.448, 2 , 14 10 , and 1.22, A) 14 10 , 2 , 1.22, 1.448 B) 14 10 , 1.22, 1.448, 2 C) 2 , 14 10 , 1.22, 1.448 D) 1.22, 2 , 14 10 , 1.448
Answer: A
Step-by-step explanation:
The ascending order of the number from smallest to largest will be 1.448, 1.22, 2, 14 10
What is Ascending order?Ascending order is a method of arranging numbers in increasing order or smallest to largest values.
We have given the values as
1.448, 2 , 14 10 , and 1.22
Here if we arrange the numbers in ascending order, we get
1.448, 1.22, 2, 14 10
Thus, The ascending order of the number from smallest to largest will be 1.448, 1.22, 2, 14 10
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Juliet rented a car for one day from a company that charges $80 per day plus $0.15 per mile driven. If she was charged a total of $98 for the rental and mileage,
for how many miles of driving was Juliet charged?
(Assume there is no tax.)
A) 15
B) 120
C) 533
D) 633
Answer:
B) 120
Step-by-step explanation:
m = miles
$98=$80+$0.15m
$98-$80=$80-$80+$0.15m
$18=$0.15m
$18/$0.15=$0.15m/$0.15
120=m
Juliet drove 120 miles for $98.
(this is a good explanation, I guess)
Answer:
Option B) 120 miles
Step-by-step explanation:
Company charges per day for a car rent = $80
and per mile driven = $0.15
Juliet rented a car for one day and she was charged a total = $98
Let Juliet traveled x miles
$80 + $0.15x = $98
0.15x = 98 - 80
0.15x = 18
x = [tex]\frac{18}{0.15}[/tex]
x = 120 miles
Juliet was charged for 120 miles driving.
Which equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4)? Select three options. y = –Two-fifthsx – 2 2x + 5y = −10 2x − 5y = −10 y + 4 = –Two-fifths(x – 5) y – 4 = Five-halves(x + 5)
Answer:
Step-by-step explanation:
Two lines are perpendicular if the first line has a slope of [tex]m[/tex] and the second line has a slope of [tex]\frac{1}{-m}[/tex].
With this information, we first need to figure out what the slope of the line is that we're given, and then we can determine what the slope of the line we're trying to find is:
[tex]5x - 2y = -6[/tex]
[tex]-2y = -5x - 6[/tex]
[tex]y = \frac{5}{2}x + 3[/tex]
We now know that [tex]m = \frac{5}{2}[/tex] for the first line, which means that the slope of the second line is [tex]m = \frac{-2}{5}[/tex]. With this, we have the following equation for our new line:
[tex]y = \frac{-2}{5}x + C[/tex]
where [tex]C[/tex] is the Y-intercept that we now need to determine with the coordinates given in the problem statement, [tex](5, -4)[/tex]:
[tex]y = \frac{-2}{5}x + C[/tex]
[tex](-4) = \frac{-2}{5}(5) + C[/tex]
[tex]-4 = -2 + C[/tex]
[tex]C = -2[/tex]
Finally, we can create our line:
[tex]y = \frac{-2}{5}x - 2[/tex]
[tex]5y = -2x - 10[/tex]
[tex]2x + 5y = -10[/tex]
Answer:
a,b,d
Step-by-step explanation:
took test on edu
Can someone help me with this word problem? I will mark anyone that offers me a useful answer the most brainiest!
I know that you have to split up the money between the 3 based on how much work they have done, but I don't understand how to do that...
Please don't answer this unless you actually understand!! Thanks! :)
Step-by-step explanation:
Hours of work- Alvin: 6 hours Theodore: 4.5 hours Simon: 1.25 hours
6+1.25+4.5= 11.75 hours Calculate the total amount of hours all of them worked together61÷11.75= $5.19 Divide the total amount of money by number of hours.5.19×6= $31.14 for Alvin, 5.19×4.5= $25.43 for Theodore, 5.19×1.25= $6.49 for Simon Multiply the number of hours worked by each chipmunk by the money made per hour.What is the center of a circle represented by the equation (x-5)2+(y+6)2=42?
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x-5)^2+(y+6)^2=42\implies [x-\stackrel{h}{5}]^2+[y-(\stackrel{k}{-6})]^2=(\stackrel{r}{\sqrt{42}})^2~~ \begin{cases} \stackrel{center}{(5,-6)}\\\\ \stackrel{radius}{\sqrt{42}} \end{cases}[/tex]
Answer:
(5, -6)Step-by-step explanation:
The equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have:
[tex](x-5)^2+(y+6)^2=42\\\\(x-5)^2+(y-(-6))^2=42[/tex]
Therefore
[tex]h=5,\ k=-6,\ r^2=42\to r=\sqrt{42}[/tex]