Answer:
4.78 × 10^-6
Hope this helped :)
Answer: 4.78 × 10^-6
Step-by-step explanation:
An athletic facility is building an indoor track. The track is composed of a rectangle and two semicircles.
a. Write a formula for the perimeter of the indoor track
P=
b. Solve the formula for x.
x=
c. The perimeter of the track is 660 feet, and r is 50 feet. Find x. Round to the nearest foot.
x=____feet
Answer:
(The image is not provided, so i draw an idea of how i supposed that the problem is, the image is at the bottom)
Ok, we have a rectangle of length x by r.
At the extremes of length r, we add two semicircles.
So the perimeter will be equal to:
Two times x, plus the perimeter of the two semicircles (that can be thought as only one circle).
The radius of the semicircles is r, and the perimeter of a circle is:
C = 2*pi*r
where pi = 3.14
Then the perimeter of the track is:
P = 2*x + 2*pi*r.
b) now we want to solve this for x, this means isolating x in one side of the equation.
P - 2*pi*r = 2*x
P/2 - pi*r = x.
c) now we have:
P = 660ft
r = 50ft
then we can replace the values and find x.
x = 660ft/2 - 3.14*50ft = 173ft
Round 496.739386253 to the nearest whole number.
Answer:
467
Step-by-step explanation:
7 is greater than 5 so the six is rounded to a 7
Hope this helped please mark me brainiest
Answer:
497
Step-by-step explanation:
If x ≥ 5, we round up.
If x < 5, we round down.
Since 7 ≥ 5, we round 496.739386253 to 497.
Function g is a transformation of the parent quadratic function f. Which statements are true about this function?
g(x) = -(x - 4)2 + 6
Select all the correct answers.
Function g reflected function facross the x-axis.
Function g translated the vertex from (0,0) to (-4,6).
For function g, as x approaches negative infinity, 8(x) approaches negative infinity.
Function g is always decreasing,
Function g is always negative.
Function g is symmetrical about the point (4,6).
Answer: Function g reflected function f across the x-axis.
For function g, as x approaches negative infinity, g(x) approaches negative infinity.
Function f is symmetrical about the point (4,6).
The correct options are Option A and Option C : Function g is reflected of function f across the x-axis. and as x approaches to the -∞, g approaches to the -∞.
Here given that the function g(x)= -(x-4)²+6
vertex of the graph of the function g is
dg/dx=0
⇒2(x-4)=0
⇒x-4=0
⇒x=4
putting x=4 in g(x) , g(4)= -(0-0)²+6=6
Hence the vertex of the graph of g is (4,6).
The parent function is f(x)= x²
here the vertex of the function is (0,0).
Option A: This option is true as the graph of function g is the inverse image of f. So, Function g is reflected of function f across the x-axis.
Option B: This option is incorrect. as the vertex of the function f is transformed to (4,6) which is the vertex of g(x).
Option C: This option is true because
[tex]\lim_{x \to- \infty} g(x)[/tex]
= [tex]\lim_{x \to- \infty} -(x-4)^2+6\\[/tex]
= -(∞-4)²+6
=-∞²+6
=-∞
Hence as x approaches to the -∞, g approaches to the -∞
Option D. This option is incorrect because
if the function is always decreasing its derivative is negative for all x∈R
dg/dx<0
⇒2(x-4)<0
⇒x-4<0
⇒x<4
so the function is decreasing for x<4 not for all x.
Option E: This option is incorrect. because g is not always rather it is positive for 4-√6 < x < 4+√6
g(x)>0
⇒-(x-4)²+6 >0
⇒-(x-4)²>-6
⇒(x-4)²<6
⇒|x-4|<√6
⇒4-√6<x<4+√6
so, g(x) is positive for 4-√6 < x < 4+√6
Option E:
This option is incorrect as g(x) is symmetrical about line x=4.
Therefore the correct options are Option A and Option C : Function g is reflected of function f across the x-axis. and as x approaches to the -∞, g approaches to the -∞.
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a −3=( a 1 ) 5 what is the value of a?
Answer:
A=[tex]\frac{-3}{4}[/tex]
Step-by-step explanation:
a−3=a1(5)
Step 1: Simplify both sides of the equation.
a−3=a1(5)
a+−3=5a
a−3=5a
Step 2: Subtract 5a from both sides.
a−3−5a=5a−5a
−4a−3=0
Step 3: Add 3 to both sides.
−4a−3+3=0+3
−4a=3
Step 4: Divide both sides by -4.
-4a/-4 = 3/-4
Your final answer is a=-3/4During the winter, the amount of water that flows down a river remains at a low constant. In the spring, when the snow melts, the amount of water increases drastically, until it decreases to a steady rate in the summer. The flow then slowly decreases through the fall into the winter. Consider the graphs shown. Which graph best represents the given situation?
Answer:
Its Graph B
Step-by-step explanation:
I got the quiz correct
how many class periods that are 3 fourth of an hour long will fit into a school day 6 and 3 fourth hours long
What is 1.4 as a fraction in simplest form explain the steps!
Answer:
7/5
Step-by-step explanation:
What is 1.4 in fraction form? 7/5 is the fraction form of 1.4. 1.4 as a Fraction in simplest form to convert 1.4 to a fraction and simplify to the lowest form.
------------
14/10 = 1.4
7 is half of 14
5 is half of 10
The simplest form of given number is [tex]\frac{7}{5} [/tex].
Given number is, 1.4
Converted into fraction, [tex]=\frac{14}{10} [/tex]
It is observed that, 2 is common in both numerator and denominator.
[tex]\frac{14}{10} =\frac{2*7}{2*5}=\frac{7}{5} [/tex]
Hence, The simplest form of given number is [tex]\frac{7}{5} [/tex].
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Please help me brainiest is award
Answer:
-3 >-5
5>-4
Step-by-step explanation:
Negative 3 is closer to zero so that statement is true. Also it's obvious 5 is greater than negative 4
hope this helps. Please mark me brainiest
Find each rate and unit rate $8.96 for 8 pounds of grapefruit?
Answer:
the answer should be 0.96
Find the lowest common multiple (LCM) of 30 and 42
Answer:
2-30,42
3-15,21
5-5,7
7-1,7
-1,1
LCM of 30 and 42 is 210
Answer:
210
Step-by-step explanation:
30*42 by HCF of 30,42
1260 by 6 =210
5. Tinh Tran is a physical therapist. He earns $49,830 a year and is
single with no dependents. The state income tax rate is 5% of
taxable income. What amount is withheld from his biweekly
pay for state income tax?
Answer:
2491.50$ oooooooooooooooooooooooo
The amount withheld from his biweekly pay for state income tax is $2491.5.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
We have been given that the physical therapist earns $49,830 a year and is single with no dependents.
To determine the amount withheld from his biweekly pay for state income tax.
Since the state income tax rate is 5% of taxable income.
So the amount withheld from his biweekly pay for state income tax as:
⇒ 5 % of 49,830
⇒ (5/100)49,830
⇒ (0.05)49,830
⇒ 2491.50
Therefore, the amount withheld from his biweekly pay for state income tax is $2491.5.
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Triangle Z is a scaled copy of Triangle M.
Select all the sets of values that could be the side lengths of Triangle Z.
a. 8, 11, and 14.
b. 10, 17.5, and 25.
C. 6, 9, and 11.
d. 6, 10.5, and 15.
e. 8, 14, and 20.
Answer:
D and E are correct
Step-by-step explanation:
Here, we want to select the set of values which could be the values of the sides of triangle z.
What we want here are sets of values which is a direct scale up value of the sets of values of triangle M:
We proceed as follows;
a. 8, 11 and 14.
This cannot be correct
Looking at the values of M, 4,7 and 10; We can see that while 4 and 7 are directly scaled up by factor 2 to give 8 and 14, by correspondence, 10 should be 20 and not 11 as in this case.
B. 10, 7.5 and 25
This cannot be correct too. Looking at the way 4 and 10
are scaled up by a value of 2.5; then the value of 7 should be scaled by 2.5 too, but 2.5 * 7 is not 7.5, so this cannot be correct
C. 6 , 9 and 11
This is not correct. In fact, we cannot identify a pattern between these numbers and their values before scaling up
D 6, 10.5 and 15
This looks correct. We can see that the values of triangle M if multiplied by 1.5 each can give these
4 * 1.5 = 6
7 * 1.5 = 10.5
and 10 * 1.5 = 15
e. 8, 14 and 20
Multiplying the sides of triangle M by 2, we can get these values.
4 * 2 = 8
7 * 2 = 14
and 10 * 2 = 20
The scale up value here is simply 2
Answer:
actually it's B, E, and D. At least that's what I got and it said it was correct.
Step-by-step explanation:
If b is the midpoint of line AC, and AC = 8x-20, find BC.
The Definition Of a Midpoint says that is B is the
midpoint of segment AC, then segment AB ≅ AC.
Since segment AB ≅ segment BC, we can setup
the equation 2(3x - 1) = 8x - 20 and we can solve from here.
Start by distributing the 3 through the parenthses on the left side.
So we get 6x - 2 = 8x - 20.
Now subtract 8x from both sides to get -2x - 2 = -20.
Now add 2 to both sides and we have -2x = -18.
Finally, dividing both sides by -2, we find that x = 9.
If x = 9, segment BC must be 3(9) - 1 or 27 - 1 which is 26.
The endpoints of AB are at A(1, -6) and B(7,-3). Find the coordinate of the midpoint M of the
segment.
Answer:
(4,-9/2)
Step-by-step explanation:
(1+7/2,-6-3/2)
(4,-9/2)
Solve for x.
[tex] - 36 + 7x = 76 - x[/tex]
x = [?]
Answer:
Hey there!
-36+7x=76-x
-36+8x=76
112=8x
x=14
Let me know if this helps :)
What is the square root of 10p^3
Answer:
Factor 10 into its prime factors
10 = 2 • 5
To simplify a square root, we extract factors which are squares, i.e., factors that are raised to an even exponent.
In our case however, all the factors are only raised to the first power and this means that the square root can not be simplified
At the end of this step the partly simplified SQRT looks like this:
sqrt (10p3)
STEP
2
:
Simplify the Variable part of the SQRT
Rules for simplifing variables which may be raised to a power:
(1) variables with no exponent stay inside the radical
(2) variables raised to power 1 or (-1) stay inside the radical
(3) variables raised to an even exponent: Half the exponent taken out, nothing remains inside the radical. examples:
(3.1) sqrt(x8)=x4
(3.2) sqrt(x-6)=x-3
(4) variables raised to an odd exponent which is >2 or <(-2) , examples:
(4.1) sqrt(x5)=x2•sqrt(x)
(4.2) sqrt(x-7)=x-3•sqrt(x-1)
Applying these rules to our case we find out that
SQRT(p3) = p • SQRT(p)
Combine both simplifications
sqrt (10p3) =
p • sqrt(10p)
Simplified Root :
p • sqrt(10p)
Overnight, the temperature in Mayville was – 4°F. But by the following afternoon, the temperature had risen 11°F. What was the temperature in Mayville that afternoon? To solve the problem, Rose added – 4+11 and came up with an answer of 7°F. Is Rose correct? Why or why not?
Answer:
She is correct. If you add 11 degrees to -4 degrees, you get 7 degrees.
Step-by-step explanation:
-4 + 11 = 7
The telephone company offers two billing plans for local calls. Plan 1 charges $32 per month for unlimited calls and Plan 2 charges $17 per month plus $0.03 per call.
Answer:
The indifference point is 500 calls.
Step-by-step explanation:
Giving the following information:
Plan 1 charges $32 per month for unlimited calls and Plan 2 charges $17 per month plus $0.03 per call.
I assume we have to determine the indifference point between the two plans.
First, we need to structure the cost formulas:
Plan 1= 32
Plan 2= 17 + 0.03*x
x= call
Now, we need to equal both formulas:
32 = 17 + 0.03x
15= 0.03x
500= x
The indifference point is 500 calls.
Plan 1= $32
Plan 2= 17 + 0.03*500= $32
Answer:
Step-by-step explanation:
WILL GIVE BRAINLIEST!!!!!!!!! SOLVE FOR X
Answer:
15 i think good luck
Step-by-step explanation:
Answer:
15°
Step-by-step explanation:
m<B: Supplementary: 180°-110°=70°
Triangles have an inner angle of 180°. Using this, you can then do:
180°-70°-(30°+20°)=60°
3x+x=60°
4x=60°
x=15°
Pls help I am so confused
What is the value of Negative 9 r minus 7 when r = 2?
Answer:
-25
Step-by-step explanation:
-9r - 7
-9(2) - 7
-18 - 7
-25
4.25 -2.5x = 14.75
I need help
[tex]\text {Hey! Let's Solve this Equation!}[/tex]
[tex]\text {\underline {The First Step is to do Keep Change Change (KCC)}}[/tex]
[tex]\text {Keep: 4.25}\\\text {Change: - into +}\\\text {Change: 2.5x into -2.5x}[/tex]
[tex]\text {\underline {The Next Step is to Flip the Equation}}[/tex]
[tex]\text {Before: 4.25+-2.5x=14.75}\\\text {After: -2.5x+4.25=14.75}[/tex]
[tex]\text {\underline {The Next Step is to Subtract 4.25}}[/tex]
[tex]\text {-2.5x+4.25-4.25=14.75-4.25=10.5}\\\text {-2.5x=10.5}[/tex]
[tex]\text {\underline {The Final Step is to Divide -2.5}}[/tex]
[tex]\text {-2.5x/-2.5=10.5/-2.5}[/tex]
[tex]\text {Remember that Dividing a Positive to a Negative will Equal a Negative.}[/tex]
[tex]\text {Your Answer Would Be:}[/tex]
[tex]\fbox {x=-4.2}[/tex]
[tex]\text {Best of Luck!}[/tex]
Hey there!☺
[tex]Answer:\boxed{x=-4.2}[/tex]
[tex]Explanation:[/tex]
[tex]4.25-2.5x=14.75[/tex]
Let's start by simplifying both sides in the equation.
[tex]4.25+-2.5x=14.75\\-2.5x+4.25=14.75[/tex]
Now we subtract 4.25 from both sides in the equation.
[tex]-2.5x+4.25-4.25=14.75-4.25\\-2.5x=10.5[/tex]
Now in our third/final step, we will divide both sides by -2.5.
[tex]\frac{-2.5x}{-2.5}= \frac{10.5}{-2.5}[/tex]
Now we simplify 10.5/-2.5.
[tex]\frac{10.5}{-2.5}=-4.2[/tex]
[tex]x=-4.2[/tex]
Hope this helps!
30 – 2а — 4) + За
Which expressions are equivalent?
Answer:
=2456
Step-by-step explanation:23456
An art studio holds beginners art classes. Each class costs $24 and there is also a one-time registration fee of $15 . You attended c number of classes and paid a total of $687. Find the number of classes you took.
The total number of classes that were taken by you was 28.
What is linear equation in one variable?The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.
According to the given question.
Registration fee for the dance class = $15
Amount of money charges for each dance class = $24
Amount of money paid for c number of classes = $687
⇒ [tex]687 = 24c + 15[/tex]
Solve the above linear equation in one variable for c.
[tex]687 = 24c + 15[/tex]
⇒ [tex]687 - 15 = 24c[/tex]
⇒ [tex]672 = 24c[/tex]
⇒ [tex]c = \frac{672}{24}[/tex]
⇒ [tex]c = 28[/tex]
Hence, the number of classes is 28.
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The temperature was -6°F. It rose so that the temperature was 0°F. What integer represents the change in temperature?
Answer:
f + 6
Step-by-step explanation:
can someone help me answer this please
Answer:
x^2 -14x+49
Step-by-step explanation:
(x-7) ^2
(x-7)(x-7)
FOIL
first ( x*x) = x^2
outer -7x
inner -7x
last -7*-7 = 49
Add these together
x^2 -7x-7x+49
Combine like terms
x^2 -14x+49
If I add 8.0g of sugar to a cup of tea, and have 2 cups of tea in the morning, how much sugar will I have consumed from drinking tea?
Answer:
1.6g
Step-by-step explanation:
1 cup of tea= 0.8g
2 cups of tea= 0.8g×2= 1.6g
James works at a department store and receive a 25% discount on his purchase he purchases some new clothes at the store and his total before the discount is $145.20 what is James total after the discount
Answer:
$108.90
Step-by-step explanation:
James pays 75% of the amount, so he pays ...
0.75 × $145.20 = $108.90
James' total after the discount is $108.90.
A submarine was situated 800 feet below sea level. If it ascends 250 feet, what is its new position?**
Answer:
650
Step-by-step explanation:
800-250=650
It's like taking a negative number and adding a positive number to it
Gertrude has 71.502 ounces of butter. How many ounces of butter does she have, rounded to the nearest hundredth?
Answer:
71.500
Step-by-step explanation:
502 is closer to 500 than 600.
Answer:
71.50
Step-by-step explanation:
This is because 2 is not up to 5, so it can't be turned into 1 and be added to 0.