Remark
I'm going to interpret this equation as
D = ut + kt² The only difference is the 2.
Solution
Subtract kt² from both sides.
D - kt² = ut Now divide by u on both sides.
[tex]\dfrac{D - kt^2}{t} = \dfrac{ut}{t}[/tex]
The t's cancel out. on the right. You are left with u on the right.
[tex]\dfrac{D - kt^2}{t} =\text{u}[/tex]
The equations 2x+7=3 and bx-10=-2 have the same solution for x. Find the value of b.
Solve both equations for x:
2x+7 = 3
2x = -4
x = -2
Plug x into the equation which contains b:
b(-2) -10 = -2
-2b = 8
b = -4
Answer:
b = -4
x = -2
To find the value of b so that the equations 2x+7=3 and bx-10=-2 have the same solution, solve the first equation for x, then use that value to solve for b in the second equation. The value of b is -4.
To find the value of b such that the equations 2x+7=3 and bx-10=-2 have the same solution for x, we need to solve the first equation for x.
Solving the equation 2x+7=3:
Subtract 7 from both sides: 2x = -4
Divide both sides by 2: x = -2
Now that we have the solution x = -2, we can plug this value into the second equation to find b:
bx - 10 = -2
Substitute x with -2: b(-2) - 10 = -2
Multiply b by -2: -2b - 10 = -2
Add 10 to both sides: -2b = 8
Divide both sides by -2: b = -4
Therefore, the value of b is -4.
What is the slope of the line that passes through the points (-2, 2), and (-4, -2)?
a.-1/2
b.2
c.-2
d.1/2
The slope would be b.2
What does 7/18 + 2/27=
The answer would be 25/54
25/54 or .46
7/18+2/27
Use the equation y = 4x to answer the questions.
The slope is 4 and the Y-Intercept is 0.
Jasper starts the month with $24 in his savings account. At the end of each week, Jasper adds $8 to the account. How much will Jasper have in his account after 10 weeks?
24 + (8·10)
24 + 80
104 dollars after ten weeks
The figure below shows the penalty box and the goal box of a soccer field. The penalty box is the largest rectangle
Part (A):
The area of the penalty box.
The dimensions of the penalty box are (15x-1) and (5x-7)
The area of rectangle = length * width
∴ The area of the penalty box = (15x-1) * (5x-7) = 75 x² - 110 x + 7
===================================================
Part (B):
The area of the goal box.
The dimensions of the goal box are (7x-1) and (x+3)
The area of rectangle = length * width
∴ The area of the goal box = (7x-1) * (x+3) = 7x² + 20x - 3
=======================================================
Part (C):
The area of the penalty box not coverd by the goal box =
The area of the penalty box - The area of the goal box =
(75 x² - 110 x + 7) - (7x² + 20x - 3) = 68 x² - 130 x + 10
is 5.3 repeating rational
Repeating decimals are considered rational numbers because they can be represented as a ratio of two integers. If a number is terminating or repeating, it must be rational if a decimal is both non terminating and non repeating, the number is irrational.
So yes.
Yes, 5.3 repeating is a rational number. It can be written as the fraction 53/9.
Explanation:Yes, 5.3 repeating is a rational number. A rational number is a number that can be expressed as a fraction, where both the numerator and denominator are integers. In this case, we can write 5.3 repeating as the fraction 53/9. The decimal 5.3 repeating means that the digit 3 repeats infinitely, so it can be written as 5.3333... In fraction form, this becomes 53/10 + 53/100 + 53/1000 + ...
Learn more about Rational numbers here:https://brainly.com/question/24398433
#SPJ3
How many 1/5 cup servings are in 3/4 of a cup of ice cream
2 factors of 36 add up to 15 What are they?
Hey there!!
What are the factors of 36?
Ans :- 1 , 36 , 2 , 18 , 3 , 12 , 4 , 9 , 6
Which of these numbers add up to 15 ?
... 12 + 3 = 15
The number are 15.
They add up to 15 and both of these are factors of 36.
Hope my answer helps!!
If the equation y = (x - 6)(x + 12) is graphed in the xy-plane, what is the x-coordinate of the parabola’s vertex? Also please show the steps. :)
x- coordinate of vertex = - 3
the vertex lies on the axis of symmetry , which is positioned at the midpoint of the zeros
find the zeros by setting y = 0
(x - 6)(x + 12) = 0 ( equate each factor to zero and solve for x )
x - 6 = 0 ⇒ x = 6
x + 12 = 0 ⇒ x = - 12
x coordinate of vertex = [tex]\frac{- 12+6}{2}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3
find two consecutive odd integers whose product is 1443
Let's x represents the first odd integer
The next consecutive integer would be represented as x+2.
So x and x+2 being multiplied together will give us 1443:
(x)(x+2)=1443
x^2+2x=1443
x^2+2x-1443=0
By solving the quadratic equation using the quadratic formula, x will equal to 37 and -39.
Since the problem says "integers", so I'm assuming two pairs of consecutive integers would be ok.
With that said you 1st pair will be: 37,39
Your second pair will be: -37,-39.
what is the least common denominator of 5/9 and 11/12?
The LCM of 5/9 and 11/12
is 36
9*4=36
12*3=36
20/36
&
33/36
To rent a certain meeting room, a college charges a reservation fee $18 and an additional fee of five dollars per hour. The chemistry club want to spend less and $78 on renting the room what are the possible numbers of hours in the chemistry club convention for the meeting room
This problem would be best modeled by an inequality.
Let t = the number of hours.
18 + 5t < 78
5t < 60
t < 12
The way the question sounds, it would not be a lessthan or equal to, because they want to spend less than 78. It would be a less than or equal problem if they said "no more than 78"
shen just bought 7 bags of 14 cookies each.he already had 9 cookies in a jar. how many cookies does shen have now??
What is the slope of y= 4x + 5
Answer:
Step-byhe slope is 4, or 4/1, and the y-intercept is 5, or (0, 5).step explanation:
[tex]\bf \stackrel{slope}{y=\stackrel{\downarrow }{4}x+5}~\hspace{5em}\begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
Anna picked 6 apples. Sabrina picked 7 times as many apples. How many apples did Sabrina pick?
Anna picked 6 apples
Sabrina picked 7 times as many apples.
Multiply the two numbers together
6 x 7 = 42
Sabrina picked 42 apples
hope this helps
~Rise Above the Ordinary
Anna picked 6 apples. Sabrina picked 7 times as many apples. How many apples did Sabrina pick?
Times, means to multiply, take the only two numbers in the problem and multiply them together.
6 x 7 = 42
~
Let’s say you plan to start a lawn-mowing business for a little extra money over the summer. A new lawn-mower costs $450. Between the gas you use and the time is takes to travel (your time is important, after all), you estimate you will incur a cost of approximately $6 per lawn you mow. If you charge $35 for each lawn you mow, how many lawns must you mow before you become profitable?
If you plan on mowing only 3 lawns per day, 5 days per week, over the summer, how long will it take to make a profit of $2,500? Do you think this is a reasonable goal? Why or why not?
Your profit per lawn is [tex]payed \minus cost[/tex] which is [tex]35 \minus 6 = 29[/tex].
If you want to be profitable, you must earn more than the cost of the lawn mower. Each mowing you earn 29$. We must divide using the formula [tex]cost \divide profit = times[/tex] where times is the amount of times you must mow lawns to be profitable. We get [tex]450 \divide 29 = 15.51...[/tex], but you can't only mow parts of a lawn! Therefore, you must mow 16 lawns to be profitable.
Your second part depends on how many weeks are in the summer.
But the answer would look like $435 per week earned, and -$450 one time cost for the lawnmower.
Part A.
You spend $6 per lawn and charge $35 per lawn, so the profit per lawn is $35 - $6 = $29. Let the number of lawns you mow be n. You earn a profit of $29 pewr laun, so you earn a profit of 29n for mowing n lawns.
29n = 450
Divide both sides by 29.
n = 450/29 = 15.517...
You must mow 16 lawns to make profit.
Part B.
3 lawns per day for 5 days per week means 15 lawns per week. Since you make a profit of $29 per lawn, you will make a profit of 15 * $29 for 15 lawns in each week. 15 * $29 = $435.
You want to make $2500 profit, but you must spend $450 on the lawn mower, so you need to earn a total of $2500 + $450 = $2950.
Let n be the number of weeks. In one week, you make $435 in profit. In n weeks, you make 435n in profit.
435n = 2950
Divide both sides by 435.
n = 6.7816...
If you work for 7 weeks, you will make at least $2500 in profit.
Since the summer vacation is longer than 7 weeks, it is a reasonable goal, but you must take into account the time it takes to mow three lawns in one day.
Please!! help me with number 7. and 9.
and I will THANK YOU!!!
7) 12 / 6
(how many party favors can he give to 6 people if he has twelve? each person can get 2)
9) 2(12)
(Each water bottle is two dollars, how many bottles did she buy? 12. 12 bottles at 2 dollars each would be $24)
how long will it take to spend 1millon if you spend 1000 per day?
It will take 1000 days to spend 1,000,000 if you spend 1,000 per day.
1000 days
Hope it helps ❤️
what is the slope of -1,-7 and 3,9
Answer:
The slope is 4.
Step-by-step explanation:
Use the slope formula.
[tex] m = \dfrac{y_2 - y_1}{x_2 - x_1} [/tex]
[tex] m = \dfrac{-7 - 9}{-1 - 3} [/tex]
[tex] m = \dfrac{-16}{-4} [/tex]
[tex] m = 4 [/tex]
331 students went on a field trip .six buses were filled and 7 students traveled in cars how many students were in each bus?
331 total students. 7 traveled by car.
331 - 7 = 324 were on buses.
There were 6 buses:
324 / 6 = 54 students on each bus.
Which variable is most important to the following problem? At 9:45 a.m. a patient’s temperature was 101.5 degrees at 10:41, the nurse took the patients temperature again and found it was 105.8 degrees, the highest ever recorded. How long did it take for the patients temperature to reach that high? A: the number of minutes it took for the to reach its peak B: the number of degrees that the temperature changed C: the date on which the previous high was recorded
Answer:
Option A is the important variable.
Step-by-step explanation:
Given is - At 9:45 a.m. a patient’s temperature was 101.5 degrees at 10:41, the nurse took the patients temperature again and found it was 105.8 degrees, the highest ever recorded.
The variable that is most important here is A: the number of minutes it took for the to reach its peak.
Firstly it is not mentioned if 10:41 is am or pm.
If its am, then such a temperature rise in less than an hour is very dangerous.
So, the important variable is option A.
Answer:
The answer is B: the number of degrees that the temperature changed.
Step-by-step explanation:
Just took the test
a fence is 702 m long. it is cut into three parts. two parts are the same length and the third is 27 m longer than either of the other two. find the length of each part
Answer:
225, 225 and 252 meters
Step-by-step explanation:
Let length of the 2 equal parts be each x m, then:-
2x + x + 27 = 702
3x = 702 - 27 = 675
x = 675/3
x = 225
So lengths of each parts are 225, 225, 252
To find the lengths of the three parts, we let the length of each of the two equal parts be 'x' and set up the equation 3x + 27 = 702. Solving for 'x' gives us that each of the two equal parts is 225 m, and the third part is 252 m.
The student is asking to find the lengths of three parts of a fence that has been cut, with two parts being equal in length and the third part being 27 m longer than the other two. Let's assume each of the two parts that are the same length is 'x' meters. Since the third part is 27 m longer, it would be 'x + 27' meters. According to the problem, the total length of the fence is 702 m.
Therefore, the sum of all three parts is:
x + x + (x + 27) = 702
Simplifying this, we get:
3x + 27 = 702
Subtract 27 from both sides:
3x = 675
Now, divide both sides by 3:
x = 225
So, the two equal parts are each 225 m long, and the third part is 225 + 27 = 252 m long.
a number is multiplied by 4. Next, 3 is added to the product, ans then 11 is substracted. If the result is 24, what is the number
Answer:
x = 6
Step-by-step explanation:
(x)(4) +3 -11 = 24
6 x 4 = 32
32 + 3 = 35
35 - 11 = 24
what property of multiplication is illustrated 4x6x10
The answer demonstrates the associative property through the multiplication of 4x6x10, resulting in 240.
Multiplication Properties Illustrated in 4x6x10:
The property of associative property is illustrated in 4x6x10. This means that changing the grouping of the numbers being multiplied does not change the result.
Step 1: Compute 4x6 = 24Step 2: Multiply 24 by 10, which gives the final result: 240.Yoko drove 522 miles in 9 hours. At the same rate, how many miles would she drive in 13 hours?
Yoko would drive 754 miles in 13 hours.
First you would have to find how many miles Yoko drives per hour so you divide 522 miles/9 hours to get 58 miles per 1 hour. Then you multiply 58 * 13 to get 754 miles.
what is 2 and 3/5 equal to in decimals
2 and 3/5 is equal to 2.6.
Being as the 2 is in front of the fraction, it is the whole number. This means in decimal form, it is to the left of the decimal point. Since there is no "fifths place" in a decimal, you must make it so it can go under the tenths, hundreths, thousanths or another place within the right side of the deciamal point. Simply multiplying 3/5 by 2/2 will give you 6/10. 6/10 as a decimal, is 0.6. Finally, add 0.6 and 2 together. Thus making 2.6 the answer.
I hope this helps!
Find the coordinates of the point of intersection of the graphs of lines with y=−2x+7 and y=0.5x−5.5
the coordinates of the point of intersection of the graphs of lines with
y=−2x+7 and y=0.5x−5.5
to find intersection we solve for x and y
We replace -2x+7 for y in the second equation
−2x+7 =0.5x−5.5
Subtract 0.5x from both sides
-2.5x + 7 = -5.5
Subtract 7 on both sides
-2.5x = -5.5 - 7
-2.5x = -12.5
divide by -2.5 from both sides
x = 5
Plug in 5 for x in y=−2x+7
y=−2(5)+7
y = -10 + 7
y = -3
The point of intersection is (5,-3)
John has a roll containing 24 2/3 feet of wrapping paper. he wants to divided it into 11 pieces, first though he must cut off 5/6 foot because it is torn. How long will each piece be?
Ok, so first you have to take the 5/6th off. This would be 24 4/6 - 5/6th which would be 23 and 5/6ths. The next step would be to turn the 5/6 into a decimal. That would be 0.83333 so 23.83 divided by 11. The answer would be 2.166363664 according the the calculator. HOPE THIS HELPS!!!
Answer:
[tex]2\frac{1}{6}[/tex] foot
Step-by-step explanation:
John has a roll containing [tex]24\frac{2}{3}[/tex] feet of wrapping paper.
He must cut off [tex]\frac{5}{6}[/tex] feet.
Now the left over wrapping paper = [tex]24\frac{2}{3}[/tex] - [tex]\frac{5}{6}[/tex]
= [tex]\frac{74}{3}[/tex] - [tex]\frac{5}{6}[/tex]
= [tex]\frac{148-5}{6}[/tex]
= [tex]\frac{143}{6}[/tex]
= [tex]23\frac{5}{6}[/tex]
He wants to divide the left over wrapping paper into 11 pieces.
[tex]23\frac{5}{6}[/tex] ÷ 11
[tex]\frac{143}{6}[/tex] ÷ 11
[tex]\frac{143}{6}[/tex] × [tex]\frac{1}{11}[/tex]
[tex]\frac{143}{66}[/tex]
[tex]\frac{13}{6}[/tex]
[tex]2\frac{1}{6}[/tex] foot
Each piece would be [tex]2\frac{1}{6}[/tex] foot long.
increase or decrease 32 pages to 28 Pages round to the nearest tenth of a percent
Final answer:
The number of pages decreased from 32 to 28, which is a difference of 4 pages. Dividing by the initial number of pages and multiplying by 100 gives a decrease of 12.5%.
Explanation:
To calculate the percentage change when the number of pages in a document decreases from 32 to 28, we follow these steps:
Find the difference between the two numbers. In this case, it is 32 pages - 28 pages = 4 pages.Divide the difference by the initial number of pages. So, we do 4 pages / 32 pages = 0.125.Multiply the result by 100 to get the percentage. Thus, 0.125 * 100 = 12.5%.Since the number of pages decreased, it is a 12.5% decrease.Therefore, there is a 12.5% decrease when a document goes from 32 pages to 28 pages.