Diana's second time was faster by 0.84 yards.
How to calculate the speed?Th speed of the first race will be:
= Distance / Time
= 300 / 65
= 4.62 yards per second
The speed of the second race will be:
= 300 / 55
= 5.46 yard per second.
The difference will be:
= 5.46 - 4.62
= 0.84 yards
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The function f(x) = (x+4)³ + 3 is one-to-one and therefore invertible. Determine f-¹. Graph both f
and f-1, along with the identity function f(x) = 2.
f-¹(x) =
The function of f(x) = (x+4)³ + 3 is one-to-one then the value of
[tex]f^{-1} (x) = \sqrt[3]{x} - 4[/tex] and,
[tex]f^{-1} (2) = -2.7401[/tex]
The function f(x) = (x+4)³ + 3
Let us assume,
y = (x+4)³ + 3
What is Invertible function?A function is said to be invertible when it has an inverse. It is represented by [tex]f^{-1}[/tex]. Condition for a function to have a well-defined inverse is that it be one-to-one and Onto or simply bijective.
Then,
y = (x+4)³ and y = 3
Therefore the inverse of y = 3 is the line x = 3
We can solve,
y = (x+4)³
The solution of Inverse function,
So,
[tex]\sqrt[3]{y} = x+4[/tex]
We can get,
[tex]x = \sqrt[3]{y} -4[/tex]
So the inverse of y is [tex]\sqrt[3]{x} -4[/tex]
f(x) = (x+4)³
So the inverse of f(x) is [tex]\sqrt[3]{x} -4[/tex]
Therefore, [tex]f^{-1}( x)[/tex] = [tex]\sqrt[3]{x} -4[/tex]
Then f(x) = 2
[tex]f^{-1} (x) = \sqrt[3]{x} - 4[/tex]
We can substitute f(x) = 2
[tex]f^{-1} (2) = \sqrt[3]{2} -4[/tex]
Since, ∛2 = 1.2599
We can substitute this value,
[tex]f^{-1} (2) = 1.2599-4[/tex]
[tex]f^{-1} (2) = -2.7401[/tex]
Therefore,
The value of ,
[tex]f^{-1} (x) = \sqrt[3]{x} - 4[/tex] and,
[tex]f^{-1} (2) = -2.7401[/tex]
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ASAP can someone help me with this will mark you brainliest
Answer:
C
Step-by-step explanation:
hope this helps!
Nine billion , two hundred forty-six million,seventy-three thousand ,one hundred eighty-nine
In digits
Answer:
9,246,073,189
Step-by-step explanation:
Answer:
9,246,793,189
Step-by-step explanation:
its 9 billion which have nine zeros in behind
and others do it by yourself
3.
The Moy family budgeted $32,650 to remodel their kitchen. They spent
$43,987. How much more or less is the amount spent than the amount
budgeted?
A $11,337 more
B $11,337 less
C $17,887 more
D $17,887 less
Answer:
A
Step-by-step explanation:
43987-32650= 11337
And it’s more
The cost of a taxi ride, in dollars, is $2 for the first quarter mile plus $0.40 for each quarter mile after that. Jameel cannot
afford to spend more than $20 on a taxi ride.
The equation 2 + 0.4(4m - 1) = 20 can be used to find m, the distance, in miles, that Jameel can travel for $20. What
is the maximum distance?
A) 13.5 miles
B 16.0 miles
C11.5 miles
(D) 14.0 miles
The maximum distance Jameel can travel is 11.5 miles
How to determine the maximum distance?The equation that determines the distance is given as
2 + 0.4(4m - 1) = 20
Subtract 2 from both sides of the equation
So, we have
0.4(4m - 1) = 20 -2
Evaluate the like terms
So, we have
0.4(4m - 1) = 18
Divide both sides by 0.4
So, we have
(4m - 1) = 18/0.4
Evaluate the quotients
So, we have
(4m - 1) = 45
Remove the bracket
So, we have
4m - 1 = 45
Add 1 to both sides of the equation
4m = 46
Divide both sides of the equation by 4
So, we have
x = 11.5
Hence, the maximum distance Jameel can travel is 11.5miles
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How do you solve this Зп – 1
Step-by-step explanation:
3n just means 3 × n
To actually solve the equation, the value of n would have to be given.
In some equations, you would have to solve for n and then answer the equation, but that's not possible with this one.
At its farthest, the earth is about 9.52 * 10 ^ 7 miles from the sun. Light travels from the sun at a speed of around 1.2 * 10 ^ 6 miles per minute. How many minutes does it take for the light to travel from the Sun to the Earth? Show your calculations and write in standard form.
The number of minutes to take for the light to travel from the sun to the earth is 7.93×[tex]10^{1}[/tex] minutes.
The distance between the earth and sun=9.52×[tex]10^{7}[/tex] miles
The speed of the light from sun=1.2×[tex]10^{6}[/tex] miles per minutes
Speed=Distance/Time
Time= Distance/Speed
Substitute the values in the equation
Time taken for the light to travel from the sun to the earth = The distance between the earth and sun ÷ The speed of the light from sun
Substitute the values in the equation
=9.52×[tex]10^{7}[/tex]÷ 1.2×[tex]10^{6}[/tex]
=(9.52÷1.2)×[tex]10^{7-6}[/tex]
=7.93×[tex]10^{1}[/tex] minutes
Hence, the time taken for the light to travel from the sun to the earth is 7.93×[tex]10^{1}[/tex] minutes
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16m² -n²
What is it factor
Answer: (4m+n)(4m-n)
Step-by-step explanation:
16m² -n²=
(4m)²-n²=
(4m)²+4mn-4mn-n²=
4m(4m+n)-n(4m+n)=(4m+n)(4m-n)
Answer:
[tex] = { \tt{16m {}^{2} - {n}^{2} }} \\ { \tt{ = {4}^{2} {m}^{2} - {n}^{2} }} \\ { \tt{ = (4m - n)(4m + n)}}[/tex]
A music club has 24 members. Each member pays monthly dues of $8.75. On the first day of the month, 16 members paid their dues. The remaining members paid their dues on the second day of the month. How much money was collected in dues on the second day of the month?
Answer:
$70
Step-by-step explanation:
$70 was collected on the second day of the month.
Please answer question 1 in the picture, I will mark brainliest
Answer:
1st one
Step-by-step explanation:
My mom is a teacher lol
7. A paper clip weighs 0.5 grams and an empty envelope weighs 6.75 grams.
Han adds paper clips one at a time to an empty envelope. Complete the table
with the weight of the envelope w(n), in grams, after n paper clips have been
added.
2012 3
a.
w(n)
6.75
The total weight of the envelop after n paper clips have been added is w(n) = 0.5n + 6.75
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let w(n) represent the total weight of the envelop with n paper clips. A paper clip weighs 0.5 grams and an empty envelope weighs 6.75 grams. Hence:
w(n) = 0.5n + 6.75
The total weight of the envelop after n paper clips have been added is w(n) = 0.5n + 6.75
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0,0 as center of dilation 1/4 and a =10,6
The new coordinates after the dilation with scale factor 1/4 is
a' = (5/2 , 3/2)
To get the new coordinates when the point is dilated is to multiply the scale factor with the coordinates of the point.
According to the question we have been given that
center of dilation = (0,0)
Scale factor = 1/4
coordinate of the point, a = (10,6)
To get the new coordinates we will multiply the given coordinates by the scale factor that is ,
a' = 1/4*(10,6)
= (10*1/4 , 6*1/4)
a' = (5/2 , 3/2)
Hence the new coordinates after the dilation is a' = (5/2 , 3/2)
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At Food Lion you can buy 5 cans of greens for $2.60 how much will it cost to buy three cans of green beans at the same unit price
What is the volume, in cubic inches, of a cylinder with a radius of 4 inches
and a height of 12 inches? (Use 3.14 for pi.)
Answer:
602.88 cubic inches
Step-by-step explanation:
Volume of cylinder = pi ×r^2×height
=3.14×4^2×12
=3.14×16×12
=602.88
The area of a square is the square of the length of a side
The area of a square is the square of the length of a side is a^2.
The quantity of space occupied within the square can be used to calculate the size of a square using mathematics. We'll go over the equation for calculating the square's area below. It is mainly known for its geometric quadrilaterals. The simplest definition of a square is a regular polygon with four equal sides. A square has all the same facts and characteristics as regular polygons.
The number of square units that are anticipated to fill a square is used to describe the area of a square. The area is typically defined as the area included by the confines of a level article or 2D figure.
Mathematical Area of Square Formula = a×a=a^2.
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Find the reference angle for -7pi/5
Answer:
When the terminal side is in the first quadrant (angles from 0° to 90°), our reference angle is the same as our given angle. This makes sense, since all the angles in the first quadrant are less than 90°. So, if our given angle is 33°, then its reference angle is also 33°.
When the terminal side is in the second quadrant (angles from 90° to 180°), our reference angle is 180° minus our given angle. So, if our given angle is 110°, then its reference angle is 180° – 110° = 70°.
When the terminal side is in the third quadrant (angles from 180° to 270°), our reference angle is our given angle minus 180°. So, if our given angle is 214°, then its reference angle is 214° – 180° = 34°.
When the terminal side is in the fourth quadrant (angles from 270° to 360°), our reference angle is 360° minus our given angle. So, if our given angle is 332°, then its reference angle is 360° – 332° = 28°.
Solve the system of equations.
3x + 48 + 32 = 9
3x+3y +32=3
2x + 4y + 32 = 8
Answer:
It will be (x=1.y=6.z=-6
Answer:
Choice b
(x = 1, y = 6, z = -6)
Step-by-step explanation:
The system of equations is
3x + 4y + 3z = 9 (1)
3x + 3y + 3z = 3 (2)
2x + 4y + 3z = 8 (3)
Subtract (2) from (1) to eliminate the 3x and 3y terms and solve for y
(1) - (2)
==> 3x + 4y + 3z - (3x + 3y +3z) = 9 - 3
==> 3x + 4y + 3z - 3x - 3y - 3z = 6
(3x-3x) + (4y-3y) + (3z-3z) = 6
4y - 3y = 6
y = 6
Subtract (3) from (1) to isolate the x term
(3x - 2x) + (4y-4y) + (3z-3z) = 9 -8
x = 1
Divide equation (2) on both sides by 32 to eliminate the coefficients
Equation (2) ÷ 3
==> (3x + 3y + 3z) / 2 = 3/3
==> x + y + z = 1 (4)
Substitute the values of x and y in Equation (4)
1 + 6 + z = 1
7 + z = 1
Subtract 7 from both sides
==> z = 1-7 = 6
Answer:
(x = 1, y = 6, z = -6)
line gh contains points G(-2,6) and H(5,-3) what is the slope of gh?
The slope of line gh is [tex]\frac{-9}{7}[/tex] .
Line Slope is a measure of the slope and direction of a line . The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of the line. The net change in the y coordinate is Δy and the net change in the x coordinate is Δx. The slope of a line can be calculated from two points on the line. Given the coordinates of two points, we can use the equation for the slope of the line which is given by [tex]m=\frac{y_2-y_!}{x_2-x_1}[/tex] .......(1) where [tex](x_1,y_1)[/tex] is the coordinate of first point and [tex](x_2,y_2)[/tex] is the coordinate of second pointWe have given two points G(-2,6) and H(5,-3) .
Putting [tex]x_1=-2,y_1=6[/tex] and [tex]x_2=-5 ,y_2=-3[/tex] in equation (1) , we get
[tex]m=\frac{-3-6}{5-(-2)} \\\\m=\frac{-9}{5+2}\\\\m=\frac{-9}{7} \\[/tex]
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I will mark brainliest, answer choices are:
Quadrant I
Quadrant 2
Quadrant 3
Quadrant 4
A"(0,2)
A"(1,-2)
Answer:
Quadrant 1
Step-by-step explanation:
Please help me, I'll give brainliest.
In below Diagram,
The length of BE is 15 cm.
It is given that length of FA is 40 cm and CD is 24 cm.Use trigonometry or similar triangles.In ΔDAC,Tan(∠DAC) = DC/ACIn ΔEAB,Tan(∠EAB) = BE/AB∠DAC = ∠EABDC/AC = BE/AB(DC)(AB) = (BE)(AC)This is equation (1).In ΔDAC,Tan(∠FCA) = FA/ACIn ΔDAC,Tan(∠ECB) = BE/BC∠FCA = ∠ECBFA/AC = BE/BC(FA)(BC) = (BE)(AC)This is equation (2).From equations (1) and (2),(DC)(AB) = (FA)(BC)24(AB) = 40(BC)AB = BC(40/24)AB = BC(5/3)In equation (2), AC can be written as the sum of AB and BC.(FA)(BC) = (BE)(AB + BC)Use the known values.40(BC) = (BE)[(5/3)BC + BC]40(BC) = (BE)[(8/3)BC]40 = BE(8/3)BE = (40/8)*3BE = 5*3BE = 15cmTo learn more about trigonometry, visit :
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rotation 90° counterclockwise about the origin
Estimating percents 19% of 72
Pleas explain how because I don’t understand this
Answer:
13.68
Step-by-step explanation:
72 * 0.19 = 13.68
19% can be converted to 19/100 or .19 to change out of a percentage. .19 is the multiplied by 72 to find 19% of 72.
For example
a fourth of something is the same as 25%.
if you want to find 1/4 of 8 you would multiply 8 by 1/4.
It is a similar concept with percentages.
sam sent a email to 3 friends on monday. each of these friends then sent a email on tuesday. on wensday each of those friends then sent a email to 3 friends write the prime factorization of the number of emails that were sent on wensday
A medical insurance policy requires Harold to pay the first $550 of her hospital expense. The insurance company will then pay 75% of the remaining expense. Harold estimates the total bill to be about $20,500. Apart from that Harold also had to pay 12% of $450 fee for prescription medications and a $250 late fee if she pays the bill after September 30. How much will Harold's total payment be if he pays on October 2nd?
Harold's total payment is $5,841.50.
What is Harold's total payment?Percentage is the fraction of a quantity that is expressed as a number out of hundred. The sign used to represent percentages is %. Percentages are a measure of frequency.
The total bill Harold would pay is the sum of the first $550, 25% of the remaining bill, 12% of the fee for prescription medications and the late payment fee since she paid after September 30.
Amount of total bill that Harold would pay = (100 - 75)% x (20,500 - 550)
25% x 19,950 = $4,987.50
Amount of the prescription medications Harold pays : 12% x 450 = $54
Total bill - $550 + $4,987.50 + $54 + $250 = $5,841.50
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PLEASE HELP ITS DUE TODAY Pleasee
[tex]scale \: from \: b \: to \: a = \frac{3}{2} \\ x = \frac{2}{3} \times 10.5 = 7[/tex]
Show that [16 ^1/4] ^3 and (16^3)^1/4 are equivalent
7,5+9287= x + 7?????
Answer:
X = 9287.5
Step-by-step explanation:
Solving steps
7.5+ 9287=x+7
Calculate
9294.5=x+7
Move the terms
-x=7-9294.5
Calculate
-x=-9287.5
Change the signs
Solution
X = 9287.5
f(x) = x² - 6x-7
g(x) = x + 1
Answer:
(-1, 0) and (8, 9)
Step-by-step explanation:
x² - 6x-7 = x + 1
x² - 7x - 8 = 0
(x - 8)(x + 1) = 0
x = -1, 8.
When x = - 1, y = 0
and x = 8, y = 9
which inequality is true
Answer:
The answer is C. 5π > 15
Step-by-step explanation:
5π = 15.7
15.7 is greater than 15
PLEASE HELP!!! I WILL GIVE BRAINLYEST!!
The dimensions of a room are given as 3.5 meters by 7.6 meters, to the nearest 10 cm. What area of carpet should be purchased to make sure it covers all the room?
Answer: Our carpet calculator will help you determine your approximate floor area in square metres. Simply measure the length and width of each room to the nearest 10cm, i.e. 5.4m x 3.7m, then enter your totals into the calculator and hit the 'calculate' button at the bottom.
For awkwardly shaped rooms (such as an L shape) divide the room into blocks, measure them separately and add them in as individual rooms.
Step-by-step explanation: