Answer:
3 hours
Step-by-step explanation:
Let k represent Kyle's balance after h hours. Let s represent Sophia's balance after h hours. Then we have ...
k = 25 +2h
s = 4 +9h
We want to find h so that k=s:
25 +2h = 4 +9h
21 = 7h . . . . . subtract 4+2h
3 = h . . . . . . . divide by 7
If both work 3 hours, they will have the same amount of money.
Write the following standard forms into exponential form 3 x 3 x 3 x 3 and 7 x 7.
Answer: 3^4, 7^2
Step-by-step explanation:
3 times itself 4 times! Seven times itself 2 times
Kane is training for a marathone. He started by running 3 miles during every training session. Each week plans to increase the distance of his run by 1/4 mile
Complete question :
Kane is training for a marathon. He starts by running 3 miles during every training session each week plans to increase the distance of his runs by 1/4 mile. Let w be the number of weeks. Write and expression to show the diatance kane runs in a training session after w weeks
Answer:
(11 + w ) / 4
Step-by-step explanation:
Given the following :
Initial miles kane plans to cover per session = 3 miles
Increase in miles covered per session = 1/4 mile per week
Hence, distance covered after w weeks :
Using the sum of an arithmetic progression formula:
Tn = a + (n - 1) d
a = first term = Initial / starting distance = 3 miles
n = nth term = number of weeks = w
d = common difference = constant increase in distance per week = 1/4
Hence, after w weeks :
= 3 + (w - 1) × 1/4
= 3 + (w/4 - 1/4)
= 3 + (w - 1) / 4
Taking L. C. M
(12 + w - 1) / 4
(11 + w ) / 4
The expression that shows the distance Kane runs in a training session after w weeks will be; (11 + w ) / 4
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that the Initial miles kane plans to cover per session = 3 miles
The Increase in miles covered per session = 1/4 mile per week
Using the sum of an arithmetic progression formula to calculate the distance covered after w weeks
Tn = a + (n - 1) d
a = first term = 3 miles
n = nth term = number of weeks = w
d = common difference = the constant increase in distance per week = 1/4
Hence, after w weeks,
= 3 + (w - 1) × 1/4
= 3 + (w/4 - 1/4)
= 3 + (w - 1) / 4
= (12 + w - 1) / 4
= (11 + w ) / 4
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Complete question :
Kane is training for a marathon. He starts by running 3 miles during every training session each week plans to increase the distance of his runs by 1/4 mile. Let w be the number of weeks. Write and expression to show the distance kane runs in a training session after w weeks.
Convert this rational number
to its decimal form and round
to the nearest thousandth.
1/7
Answer:
0.143
Step-by-step explanation:
1) convert to decimal form: 0.142857
2) rounding to nearest thousandth (3rd decimal place)
3) number is higher than 5 so it rounds up to 0.143
Use the fraction bar interactive to find the difference: One-third minus StartFraction 5 over 6 EndFraction
Answer:
-1/2
Step-by-step explanation:
Answer:
common denominator
6
1/3 - 5/6 difference
-1/2
Step-by-step explanation:
hope I wasn't to late
have a good day guys
:)
Your car's gas tank is 3/4 full before you leave for your trip. When you stop at the gas station, the tank is only 1/12 full. Show the amount of change as a rational number.
Answer:
2/3
Step-by-step explanation:
9 = -3 + n + 2n what does n equal ?
Step-by-step explanation:
9=-3+n+2n
9+3=n+2n
12=3n
n=12/3
n=4
[tex]9 = - 3 + n + 2n[/tex]
now let's flip this equation to make things easier[tex] - 3 + n + 2n = 9[/tex]
now move -3 to the other sidewhen we move -3 to the other side it turns into positive 3[tex]n + 2n = 9 + 3[/tex]
now add the values on both sidesn + 2n will be equal to 3n and 9 + 3 will be equal to 12[tex]3n = 12[/tex]
now move 3 to the other sidethe multiplication sign that binded 3 and n together will change into division when moved to the other side[tex]n = \frac{12}{3} [/tex]
when we divide 12 and 3 we will get 4[tex]n = 4[/tex]
so final answer is 4hope that helps !what is the distance between (7, -2) and (3,1) pls help fast
Answer:
it would be 5
Step-by-step explanation:
. Rahul has 260 coins of Rs. 1, Rs.2 and Rs.5 altogether. The total value of the money is Rs.309. The number of Rs.2 coins is three times the number of Rs.5 coins. Find the number of coins of each type.
Sara is 7 years older than Sushil. June is 4 years younger than Sushil. If the total of their ages is 87, how old is the eldest of them?
Answer:
76
Step-by-step explanation:
Answer:
We have:
a) Sushi+7=Sara
b) June=Suhi-4
c) Sushi+Sara+June=87
3 equations with 3 variables, we can solve it.
we can introduce in a) and b) in c) and we get: Sushi+Sushi+7+ Sushi-4=87
3 sushi+3=87 which gives:
3 sushi= 87-3=84
sushi=84/3=28
Sara= sushi+7 (from b)= 35
June= sushi-4=24
We can check 24+35+28=87 All good
Step-by-step explanation:
What is the answer to this question?
Answer:
(-6,300)
Step-by-step explanation:
Answer:
(-6,300)
Step-by-step explanation:
(x,y)
then:
x = -6
y = 300
then:
(-6 , 300)
Gas mileage is the number of miles you can drive on a gallon of gasoline. A test of a new car results in 460 miles on 20 gallons of gas. What is the car's gas mileage?
Answer:
23
Step-by-step explanation:
because 460 divided by 20 is 23 so the car gets 23 mpg because 460 represents miles and 20 represents gallons of gas
The car's gas mileage is 23 if the test of a new car results in 460 miles on 20 gallons of gas.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
Gas mileage is the number of miles you can drive on a gallon of gasoline.
A test of a new car results in 460 miles on 20 gallons of gas.
Let x be the car's gas mileage.
The value of the x can be found as follows:
x = 460/20
x = 23
20 gallons of gas and 460 miles are represented by the numbers.
Thus, the car's gas mileage is 23 if the test of a new car results in 460 miles on 20 gallons of gas.
Learn more about the fraction here:
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What effect does decreasing the temperature of a room have on a lifespan of a battery?
Which variable is highlighted in red, bolded tex?
This question is incomplete. There are options in the question (from reference) and no highlight in the red bolded text in the question.
What effect does decreasing the temperature of a room have on a lifespan of a battery?
Which variable is highlighted in red, bolded tex?
a . Independent
b . Dependent
c . Control
d . None
But the answer to both the independent and dependent variables will be provided and explained in detail.
Answer:
Independent variable: decrease in temperature
Dependent variable: lifespan of battery
Step-by-step explanation:
The independent variable in an experiment is defined as the variable that can be changed or manipulated in order to find an outcome while the dependent variable is defined as the variable that is influenced by the changes in the independent variable.
In the given example, a decrease in temperature is the dependent variable as it is changing and the lifespan of battery is the dependent variable as it is responding to the independent variable ?9decrease in temperature).
what is an equation of the line that passes through the points (4,-6) and (8,-4)
Answer:
[tex]y = \frac{1}{2} x - 8[/tex]
Step-by-step explanation:
The equation of a line is usually written in the form of y=mx+c, where m is the gradient (also known as slope) and c is the y-intercept (the point through which the line cuts through the y-axis).
[tex]\boxed{gradient = \frac{y1 - y2}{x1 - x2} }[/tex]
Using the gradient formula above,
[tex]m = \frac{ -4 - ( - 6)}{8 - 4} \\ m = \frac{ - 4 + 6}{4} \\ m = \frac{2}{4} \\ m = \frac{1}{2} [/tex]
Substitute the value of m into the equation:
y= ½x +c
To find the value of c, substitute a pair of coordinates.
When x=4, y= -6,
-6= ½(4) +c
-6= 2 +c
c= -6 -2 (-2 on both sides)
c= -8 (simplify)
Thus, the equation of the line is y= ½x -8.
what is the square of 3844
Answer:62
Step-by-step explanation:
62^2
Use the distributive property to find the product
Answer:
1st one: -24a-6b-36c
2nd one: 14mn-12m
Step-by-step explanation:
1st one: Multiply '-6' w/ '4a', 'b', and '6c'
2nd one: Multiply '2m' w/ '7n' and '-6'
Write 15 less than twice a number
Answer:
2x-15
Step-by-step explanation:
2x-15
Jane builds a ramp made of a triangular prism and a rectangular prism. What is the volume
of the ramp?
7.5 m3
11.5 m
1 m
4 m
28 m
2 m
3.5 m
15 m
Answer:11.5
Step-by-step explanation:I’ve done this in a test before and that is the correct AnSwEr
yesterday jack drove 33 1/2 miles. He used 1 1/4 gallons of gasloine
Point A (-8, 7) and Point B (6,-9) form a line segment on a coordinate plane. What is the midpoint of line segment AB
Answer:
-1,-1
Step-by-step explanation:
it is the midpint (-1,-1)
Answer:
( -1 , -1 )
Step-by-step explanation:
( -8 + 6 / 2 ) , ( 7 + -9 / 2)
( -2 / 2) , ( -2 / 2)
( -1 , -1 )
Solve the equation for the variable.
[tex] - 4v - 9 = 3v + 5[/tex]
v = [?]
Answer:
-4v -9 = 3v +5
=) -4v -3v = 5 +9
=) -7v =14
=) v = 14/ -7
V = -2
[tex]6 \times x = - 24[/tex]
What is the missing number?
What is the domain of the relation? {(−4.5, 0), (−3, 9), (0.9, 0), (4, −7.8), (4, 0), (17, 3)}
{0.9, 4, 17}
{−7.8, 0, 3, 9}
{−4.5, −3, 0.9, 4, 17}
{−4.5, −3}
Answer:
Domain of the relation is Option (c) : {−4.5, −3, 0.9, 4, 17}
If m∠2 = 125°, m∠12 = 37° and m∠18 = 102°, find the measure ∠1 = f.m∠7 = k.m∠13 = b.m∠3 = g.m∠8 = l.m∠14 = c.m∠4 = h.m∠9 = m.m∠15 = d.m∠5 = i.m∠10 = n.m∠16 = e.m∠6 = j.m∠11 = o.m∠17 =
Answer:
Step-by-step explanation:
1). Since, m∠2 + m∠1 = 180° [Supplementary angles]
125° + m∠1 = 180°
m∠1 = 180° - 125°
m∠1 = 55°
2). Since ∠7 ≅ ∠12 [alternate interior angles]
m∠7 = m∠12 = 37°
3). m∠3 = m∠18 = 102° [Alternate exterior angles]
4). m∠8 + m∠3 + m∠7 = 180°
m∠8 + 102 + 37 = 180
m∠8 = 41°
5). m∠14 = (m∠7 + m∠8) [Alternate angles]
m∠14 = 37 + 41 = 78°
6). m∠4 = 180° - m∠3 [Linear pairs]
= 180 - 102
= 78°
7). m∠9 = m∠3 = 102° [Vertical angles]
8). m∠15 = m∠2 [Alternate exterior angles]
= 125°
9). m∠5 = m∠15 [Corresponding angles]
= 125°
10). m∠10 + m∠5 = 180° [Sum of interior angles on one side of the transversal]
m∠10 = 180 - 125
= 55°
10). m∠16 = m∠10 = 55° [Vertical angles]
11). m∠6 = m∠10 = 55° [Alternate interior angles]
12). m∠11 = m∠15 = 125°
13). m∠17 = m∠14 = 78° [Vertical angles]
The answers are given as follows
Given that
a║b
m∠2 = 125°
m∠12 = 37°
m∠18 = 102°
From the identity of supplementary angles
m∠1 + m∠2= 180°
So m∠1 = 180° - 125° = 55°
m∠7 =m∠12 = 37° (Interior opposite angles )
m∠3 = m∠18=102° (Alternate Exterior angles )
m∠8 = 180° - m∠3 -m∠7 = 180°- 139° = 41°
m∠14 = m∠7+ m∠8= 37° + 41° = 78° ( Alternate opposite angles)
So m∠13 = 180° -78° = 102° (linear pair)
m∠4= 180° - m∠3 = 180° - 102° = 78°
m∠9 =180° - m∠4 = 180° - 78 = 102° (vertically opposite to m∠3)
m∠15 = m∠2 = 125° (Alternate exterior angles)
m∠5 =m∠15 = 125° (Corresponding Angles )
m∠10 = 180° -125° = 55°
m∠16 = m∠10 =55° ( Vertically Opposite Angles)
m∠6 = m∠10 =55° (Alternate interior angles)
m∠11 = 180 ° - m∠6° - m∠7° = 180° - 55° - 37° = 88°
m∠17 = 180° - m∠13 = 180° -102° = 78 °
For more information please refer to the link below
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Find the value of x in each case:
Answer:
x=15
Step-by-step explanation:
5x+(180-9x)+(180-8x)=180
total of a triangle angles is 180
Answer:
15°
Step-by-step explanation:
Step 1:
180° - 8x + 5x + 180° - 9x = 180° Sum of Triangle
Step 2:
360° - 12x = 180° Algerbra
Step 3:
- 12x = 180° Algerbra
Step 4:
12x = 180° Algerbra
Answer:
x = 15°
Hope This Helps :)
- If there are 12 inches in a foot, what is 4,096 cubic inches converted to cubic feet? a. 28.44 ft3 c. 2.370 ft b. 341.33 ft3 d. 4.096 ft3
Step-by-step explanation:
2.370.
One cubic foot equals 1728 cubic inches. So, to convert from cubic inches to cubic feet you should divide your cubic inches figure by 1728.
I hope it helps!
Simplify the expression: 4 + 10x + 5 - 9x
[tex]\text {Hello! Let's Solve this Equation!}[/tex]
[tex]\text {In order to Simplify this Equation you must subtract}[/tex] [tex]\text { it with the same match as it. Let me show what I mean.}[/tex]
[tex]\text {\underline {Subtract}}[/tex]
[tex]\text {10x-9x=1x=x}[/tex]
[tex]\text {\underline {Add}}[/tex]
[tex]\text {4+5=9}[/tex]
[tex]\text {Your Answer would be:}[/tex]
[tex]\fbox{x+9}[/tex]
[tex]\text {Best of Luck!}[/tex]
Hey there!☺
[tex]Answer:\boxed{x+9}[/tex]
[tex]Explanation:[/tex]
[tex]4+10x+5-9x[/tex]
Let's simplify.
[tex]4+10x+5+-9x[/tex]
Now let's combine like terms.
[tex](10x+-9x)+(4+5)[/tex]
[tex]x+9[/tex]
Hope this helps!
which graph represents The solution to
6x-2x5X +7
Answer:
Well where are the options for the graphs?
Simplify the expression: 2( 5 t + J) + 3( 2t + 4 J )
Answer:
16t + 14J
Step-by-step explanation:
1) First, you have to multiply the numbers
New Expression: 10t + 2J + 6t + 12J
2) Now, you have to find the like terms and add them together
New Expression: 16t + 14J
Hope this helps!
A yard has a perimeter of 400 feet. If eight times the length of the yard equals seventeen times the width, what are its dimensions?
Answer:
Length of the rectangular yard = 136 feet
Width of the rectangular yard = 64 feet
Step-by-step explanation:
Let
Width = 17 × width
Length = 8 × length
8l = 17w
l = 17w/8
Perimeter of a rectangular yard = 2(length + width)
400 = 2(17w/8 + w)
400 = 34w/8 + 2w
400 = 17/4w + 2w
400 = 17w+8w/4
400 = 25w/4
Cross product
1600 = 25w
Divide both sides by 25
w = 1600/25
= 64 feet
Recall,
l = 17w/8
= 17*64 / 8
= 1088/8
= 136 feet
Length of the rectangular yard = 136 feet
Width of the rectangular yard = 64 feet
State if the given functions are inverses. f(x) = 1/x + 3 g(x) = 4/x + 2
Answer:
they are not inverses
Step-by-step explanation:
f(1) = 1/1 +3 = 1 +3 = 4
g(4) = 4/4 +2 = 1 +2 = 3 ≠ 1
If the functions were inverses, we would have g(f(1)) = 1, which we do not.
The given functions are not inverses.
_____
The same would be true if your functions were
f(x) = 1/(x+3) and g(x) = 4/(x+2)
f(1) = 1/(1+3) = 1/4
g(1/4) = 4/(1/4 +2) = 4/(9/4) = 16/9 ≠ 1