Answer: the correct option is
(D) [tex]c=\dfrac{d+ab}{a}.[/tex]
Step-by-step explanation: We are given to solve the following equation for the value of c :
[tex]a(c-b)=d~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To solve the given equation for c, we need to take c on one side and all other values on the other side of the equation.
The solution for c of equation (i) is as follows :
[tex]a(c-b)=d\\\\\Rightarrow ac-ab=d\\\\\Rightarrow ac=d+ab\\\\\Rightarrow c=\dfrac{d+ab}{a}.[/tex]
Thus, the required value of c is [tex]c=\dfrac{d+ab}{a}.[/tex]
Option (D) is CORRECT.
Ken and Hamid run around a track. It takes Ken 80 seconds to complete a lap. It takes Hamid 60 seconds to complete a lap. Ken and Hamid start running at the same time from the start line. How many laps will they each have run when they next meet on the start line?
The correct answer is:
Ken will have run 3 laps and Hamid will have run 4.
Explanation:
To find this, we first find the number of seconds that will have passed when they meet again. We use the LCM, or least common multiple, for this. First we find the prime factorization of each number:
80 = 10(8)
10 = 5(2)
8 = 2(4)
4 = 2(2)
80 = 2(2)(2)(5)(2)
60 = 10(6)
10 = 5(2)
6 = 2(3)
60 = 2(2)(3)(5)
For the LCM, we multiply the common factors by the uncommon. Between the two numbers, the common factors are 2, 2 and 5. This makes the uncommon 2, 2, and 3, and makes our LCM
2(2)(5)(2)(2)(3) = 240
This means every 240 seconds they will both be at the start line.
Since Ken completes a lap in 80 seconds, he completes 240/80 = 3 laps in 240 seconds.
Since Hamid completes a lap in 60 seconds, he completes 240/60 = 4 laps in 240 seconds.
Ken will have run [tex]3[/tex] laps and Hamid will have run [tex]4[/tex] laps when they next meet on the start line.
Take LCM of [tex]80,60 =240\\[/tex]
After every [tex]240[/tex] seconds they will both be at the start line.
So in [tex]240[/tex] seconds Ken covered
[tex]\dfrac{240}{80}=3laps\\[/tex]
So in [tex]240[/tex] seconds Hamid covered
[tex]\dfrac{240}{60}=4laps\\[/tex]
Ken will have run [tex]3[/tex] laps and Hamid will have run [tex]4[/tex] Laps.
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Write five expressions equivalent to 20x + 100
1x+5 2x+10 3x+15 4x+20 5x+25
Step-by-step explanation:
To write expressions equivalent to 20x + 100, we can use factoring, distributing, and properties of equality. Examples include 4(5x + 25), 10(2x + 10), and three other variations, all of which maintain the original value of the expression.
To write five expressions equivalent to 20x + 100, we can apply various mathematical techniques such as factoring, distributing, adding/subtracting terms, or using properties of equality. Here are five different equivalent expressions:
4(5x + 25)10(2x + 10)(100x + 500) \/ 520(x + 5)200(x/10 + 5)The equivalence of these expressions to 20x + 100 remains intact because they are simply restructured using basic algebraic principles without changing the value.
What’s the smallest value of .50, .00567, .055, and .05
A gas station charges $2.20 for each gallon of gasoline how we paid $12.10 for gasoline how many gallons of gasoline did harry bye
what is the slope of the line determined by the cordinates (2,3) and (-6,-4)
Solve the formula for the bold variable.
V=lWh W- is the bold variable
The formula V=lWh is solved for W by dividing both sides of the equation by lh, providing the solution W = V / lh. This is a simple algebraic operation used for isolating the variable we're solving for, which is W in this case.
Explanation:The question asks to solve for the variable, W, in the formula V =lWh, where V represents volume, l represents length, h represents height, and W is the width we are solving for. To isolate W, you need to perform some algebraic operations. Let's go step by step:
First, we will divide both sides of the equation by l and h. So it becomes, W = V / lhThat's it! Now, the formula is solved for W.Remember, in algebra, the main goal is to isolate the variable we're trying to find on one side of the equation, which in this case is W.
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solve for 42-49 / (21-14) X 5+6
If you have 110 dollars and you rent a car that charges you 20 cents per mile, how many miles can you travel?
Is the answer to -8.8-3.4 positive or negative? I know. It is 12.2 but I don't know if it's -12.2 or +12.2
josh is inviting his friends to a party. he has 42 granola bars and 56 fruit drinks, and he wants to give the same number of each item to each friend.
Answer:
Number of granola bars that Josh gave to each of his friend =3
Number of fruit drinks that Josh gave to each of his friend =4
Step-by-step explanation:
Number of granola bars with Josh = 42
Number of fruit drinks with Josh = 56
He wants to give the same number of granola bars and fruit drinks to each friend.
To find : Number of granola bars and fruit drinks Josh give to each friend.
First, find HCF of 42 and 56 .
[tex]42=2\times 3\times 7\,,\,56=2^3\times 7[/tex]
Therefore, HCF ( 42, 56 ) = Highest common factor of 42 and 56 = 14
Number of granola bars that Josh gave to each of his friend = Number of granola bars with Josh / HCF ( 42, 56 )
= 42/14 = 3
Number of fruit drinks that Josh gave to each of his friend = Number of fruit drinks with Josh / HCF ( 42, 56 )
= 56/14 = 4
Which is true of a geometric plane? A) one-dimensional B) two-dimensional C) three-dimensional Eliminate D) no dimensions, only position
The geometric plane is two-dimensional since there are two variables.
A geometric plane is a plane which is a flat surface.
The general equation of a plane is :
ax + by + c = 0
Here x and y are variables.
Since there are two variables, the plane is two dimensional.
Or in other words, there are two directions for the plane.
So the geometric plane is two-dimensional.
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How do you find the area of a triangle
If 2x2 - x + 6 is subtracted from x2 + 3x - 2, the result is
x² + 2x - 8
x² - 4x + 8
-x² + 2x - 8
-x² + 4x - 8
Answer:
x^2 + 3x - 2 - (2x^2 - x + 6) =
x^2 + 3x - 2 - 2x^2 + x - 6 =
-x^2 + 4x - 8
the answer is 8
Someone please help. I'll mark you as brainliest :)
Martin starts at 300 and counts by fives to 420. What are the last 6 numbers Martin will say?
87,628 divided by 931
12−5x−4kx=y solve for x
Answer:
The value of the equation is [tex]x=\frac{12-y}{5+4k}[/tex].
Step-by-step explanation:
Consider the provided equation.
[tex]12-5x-4kx=y[/tex]
We need to solve the provided equation for x.
Subtract 12 both side.
[tex]12-12-5x-4kx=y-12[/tex]
[tex]-5x-4kx=y-12[/tex]
Take -x common as shown:
[tex]-x(5+4k)=y-12[/tex]
Divide both sides by 5+4k.
[tex]-x=\frac{y-12}{5+4k}[/tex]
[tex]x=\frac{-y+12}{5+4k}[/tex]
[tex]x=\frac{12-y}{5+4k}[/tex]
Hence, the value of the equation is [tex]x=\frac{12-y}{5+4k}[/tex].
Allison has 3 containers with 25 crayons in each.She also has 4 boxes of markers with 12 markers in each box.She gives 10 crayons to a friend. How many crayons and markers does Allison hace now?
How can I show my work for 257x66
The radius of a DR.PEPPER can is 3 cm and the height is 12 cm. What is the distance from the center of the bottom of the can to the edge of the top of the can?
what is the GCF of 20,36 and 72
A(n)___
is a letter used as a placeholder for an unknown value.
how to solve the equation 9v = 8 + v
The expression 625(1−x) gives the discounted price of a television, where x is the percent of the discount written in decimal form. What does the 625 represent in the expression?
the original price of the television
the percent of the original price being paid the discounted price of
the television
the percent of discount
took the test: Original price of the television
1 part sugar and 4 parts of water she uses 3/4 cup of sugar
A cashier has only one-dollar bills, quarters, and dimes. List all the ways you could receive $2.50 in change
12+4n>44 or 10-12n>-38
Worker bees can travel at 24 km/h how fast can a worker bee travel in miles per hour
3 Questions Math! HELP!!!
Add using a number line.
56+(−116)
Drag and drop the word SUM to the correct value on the number line.
----------------------
Add 34+(−212) using the number line.
Select the location on the number line to plot the sum.
---------------------
What is the sum?
1.3+(−2.4)
Enter your answer, as a decimal, in the box.
Adding a negative number on a number line is equivalent to subtracting the absolute value of that number. Thus, 56+(−116) = -60, 34+(−212) = -178 and 1.3+(−2.4) = -1.1
Explanation:When you are adding a negative number on a number line, you are essentially performing a subtraction operation. Let's look at the three problems you've posted:
1. 56+(−116): Start at positive 56 on the number line and then move 116 steps to the left because we're adding a negative number. Your final position will be -60. So, 56+(−116) equals -60.
2. 34+(−212): Similarly, start at 34 on the number line and move 212 spaces to the left which results a value of -178. Therefore, 34 + (-212) = -178.
3. 1.3+(−2.4): Starting at 1.3 on the number line, if we move 2.4 steps to the left we end up at -1.1. So, 1.3 + (-2.4) = -1.1
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What is an even radicand in Algebra 2/ Trig? Please provide an example as well.