Answer:
[tex]\large\boxed{b=0}[/tex]
Step-by-step explanation:
[tex]4b+6=2-b+4\qquad\text{combine like terms}\\\\4b+6=(2+4)-b\qquad\text{add}\ b\ \text{to both sides}\\\\5b+6=6\qquad\text{subtract 6 from both sides}\\\\5b=0\qquad\text{divide both sides by 5}\\\\b=0[/tex]
Hello!
Answer:
[tex]\boxed{b=0}\checkmark[/tex]
The answer should have a positive sign.
Step-by-step explanation:
First, switch sides and group like terms.
4b+6=-b+2+4
Then, add numbers from left/right.
2+4=6
4b+6=-b+6
Subtract by 6 both sides of an equation.
4b+6-6=-b+6-6
Simplify.
4b=-b
Next add b both sides of an equation.
4b+b=-b+b
Simplify.
5b=0
Therefore, you divide by 5 from both sides of an equation.
5b/5=0/5
Finally, you simplify and solve to find that answer is.
0/5=0
b=0 is the correct answer.
Hope this helps!
Have a nice day! :)
-Charlie
Thank you so much!
Which graph correctly represents the equation y=−4x−3?
GUYS PLEASE HELP ME IAM NOT TRYING TO FAIL SUMMER SCHOOL and will offer 40 points for who ever helps me with the next 3 problems and will give brainlest
The graph at option 4 represents the given equation y = -4x - 3 correctly. This is obtained by calculating the slope and finding the y-intercept.
What is the slope of a line with two points?The slope of a line given by
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
The ratio of the difference between y-coordinates of two points on the line to the difference of their x coordinates.
Calculation:The equation is y = -4x - 3
On comparing the equation with the slope-intercept form y = mx + c,
m = -4 and y-intercept c = -3.
Since the y-intercept is -3, the graphs at options 1 and 2 do not represent this equation. So, the remaining graphs may represent the given equation.
Finding the slope for the points in the other two graphs:The graph at option 3 has a line with two points (2, 5) and (0, -3)
So, the slope is
m = [tex]\frac{-3-5}{0-2}[/tex]
= 4
Thus, it is not the same as the slope of the given equation.
The graph at option 4 has a line with two points (-2, 5) and (0, -3)
So, the slope is
m = [tex]\frac{-3-5}{0+2}[/tex]
= -4
Thus, the line shown in the graph at option 4 has a slope of -4 and the y-intercept is -3. These are the same as the given equation. So, option 4 is correct.
Therefore, the graph at option 4 is the correct representation of the given equation.
Learn more about the graph of an equation in a slope-intercept form here:
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The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard deviation of 5 points. About what percent of students have scored between 60 and 65 points?
Answer: The percent of students have scored between 60 and 65 points is 34.13%
Step-by-step explanation:
Given : The points obtained by students of a class in a test are normally distributed with a mean of 60 points and a standard deviation of 5 points.
i.e. [tex]\mu=60\ \ \ \sigma=5[/tex]
Let x denotes the points obtained by students of a class in a test .
Now , the probability that the students have scored between 60 and 65 points :-
[tex]P(60<x<65)=P(\dfrac{60-60}{5}<\dfrac{x-\mu}{\sigma}<\dfrac{65-60}{5})\\\\= P(0<z<1)\ \ \ [\because z=\dfrac{x-\mu}{\sigma}]\\\\= P(z<1)-P(z<0.5)\ \ \ [\because\ P(z_1<Z<z_2)=P(Z<z_2)-P(Z<z_1)]\\\\=0.8413-0.5=0.3413[/tex]
[tex]=34.13\%[/tex]
Hence, the percent of students have scored between 60 and 65 points is 34.13%.
Charlene's parents deposit $500 in an account on the day she is born. The account earns a high interest rate of 9.2% compounded quarterly because Charlene is not allowed to access the money until her 22nd birthday. How much money will Charlene have on her 22nd birthday?
Answer:
about A+=+2000%281%2B+0.023%2F1%29%5E%281%2A18%29+=+2000%2A1.023%5E18= $3,011.56 thats my math
Step-by-step explanation:
Answer:
$3,698.50
Step-by-step explanation:
When making a compound interest rate this means that the interests generated are taken into consideration when creating new interests in the next period, now there are 4 quarterly periods on a year, this means there are 88 periods in the 22 years that the account will grow, you just have to do the math:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where n is the number of cycles per year and nt is the number of cycles over the years.
We just have to put the values into the formula:
[tex]A=500(1+\frac{.092}{4})^{22*4}[/tex]
[tex]A=500(1+\frac{.092}{4})^{88}[/tex]
[tex]A=$3,698.50[/tex]
División de polinomios(a²+3a+2)÷(a+1)
Answer:
a + 2
Step-by-step explanation:
Given
[tex]\frac{a^2+3a+2}{a+1}[/tex] ← factor the numerator
= [tex]\frac{(a+1)(a+2)}{a+1}[/tex]
Cancel the factor (a + 1) on the numerator/denominator
= a + 2 ← quotient
What is -2^2? I've been getting mixed results from people against calculators.
Answer:
-4
Step-by-step explanation:
Technically, the negative sign is treated as multiplying by -1, which is then separate from the 2. This equation can also be rewritten as [tex]-1 * 2^2[/tex], which would be simplified to [tex]-1 * 4[/tex] and then [tex]-4[/tex].
It depends on how the parenthesis is like. -(2)^2 will equal -4 while (-2)^2 equals 4. But the answer will most likely be 4 because they tend to make sure to put parenthesis if they want the answer to be -4. (Calculators are programmed differently which is why you're getting mixed answers.)
Match each vocabulary word to its correct definition:
1.
Cubic Polynomial--
A cubic polynomial is a polynomial of degree three.
2.
End behavior--
The end behavior of a function is it's behavior when x tends to infinity in both the directions i.e. when x tends to minus infinity and when x tends to plus infinity.
3.
Irreducible--
A polynomial is said to be irreducible if it can't be reduced i.e. it cannot be factored.
4.
Leading coefficient--
It is the coefficient of the highest degree term existing in the expression.
5.
Leading term--
It is the term with the highest degree.
6.
quartic polynomial-
A quadratic polynomial is a polynomial of degree 4.
7.
Zeros of polynomial--
The zeros of a polynomial are all the possible values of x at which the polynomial expression is equal to zero.
Which of the following is a trinomial?
O c2 + C + 6
o c2 - 16
0-80
O c3 + 402 – 120 + 7
What are the values of a, b, and c in the quadratic equation 0 =
x2 – 3x - 2?
a = 1, b = 3, c = 2
a=, b = -3,C=-2
a = 1, b = 3, c= 2
a = 1.0= -3, c = 2
Answer:
a=1, b = -3, c=-2
Step-by-step explanation:
The quadratic equation is in the form
a[tex]x^{2}[/tex] + bx +c = 0
Using the given equation
1[tex]x^{2}[/tex] -3x -2 = 0
We can see that
a=1 b=-3 c=-2
A gardener makes a new circular flower bed. The bed is fourteen feet in diameter. Calculate the circumference and the area of the circular flower bed.
Answer:
The circumference is:
[tex]C = 43.98\ ft[/tex]
The area is:
[tex]A=153.94\ ft^2[/tex]
Step-by-step explanation:
The circumference of a circle is calculated using the following formula
[tex]C = \pi d[/tex]
Where C is the circumference and d is the diameter of the circle.
In this case we know that
[tex]d = 14\ ft[/tex]
Therefore the circumference is:
[tex]C = \pi *14[/tex]
[tex]C = 43.98\ ft[/tex]
The area of a circle is calculated using the following formula
[tex]A=\pi(\frac{d}{2})^2[/tex]
Where d is the diameter of the circle.
Then
[tex]A=\pi(\frac{14}{2})^2[/tex]
[tex]A=\pi(7)^2[/tex]
[tex]A=49\pi[/tex]
[tex]A=153.94\ ft^2[/tex]
The circumference of the flower bed is approximately 43.96 feet and the area is approximately 153.86 square feet.
Explanation:The gardener's circular flower bed has a diameter of 14 feet. The formula to calculate the circumference of a circle is C=πd where 'd' represents the diameter. Therefore, by substituting the given diameter, we get C = 3.14 * 14 = 43.96 feet approximately.
The area of the circle can be calculated by using the formula A=πr², where 'r' represents the radius of the circle. The radius is half of the diameter, that is 14/2 = 7 feet. So, A = 3.14 * 7² = 153.86 square feet approximately.
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PLEASE HELP WILL GIVE BRAINLIEST
Which of the sets of ordered pairs represents a function?
A = {(–5, 5), (–2, 2), (2, –2), (5, –5)}
B = {(4, 2), (3, –2), (9, 4), (11, –3)}
Only A
Only B
Both A and B
Neither A nor B
Answer:
The answer would be, both A. and B.
Answer:
both a and b
Step-by-step explanation:
If a graph of y=-3x+ 5 were changed to a graph of y = 2x + 5, how would the
slope change?
A. The slope of the new graph would become less steep.
B. More information is needed to determine the change.
C. The slope would remain the same.
D. The slope of the new graph would become steeper.
Alright (so what I did was type this into desmos and it was the exact same line but it was the other way around so it is) C
Changing from y = -3x + 5 to y = 2x + 5 would make the slope steeper.
The slope of the new graph would become steeper.
When changing from y = -3x + 5 to y = 2x + 5, the original slope of -3 increases to 2, making the new graph steeper.
Therefore, the correct answer is D. The slope of the new graph would become steeper.
Hernando ate 2/8 of a pizza for a dinner. He gave his 6 friends the rest of the pizza and told them to share it equally
Answer:
umm his friends each got 1/8
Step-by-step explanation:
hernando ate 2/8 meaning 8-2=6= 6/8
6/8 / 6 = 1/8
:D
I guess this what you want
After Hernando ate [tex]\frac{2}{8}[/tex] of the pizza, the remaining pizza when divided equally among his friend leaves each friend with [tex]\frac{1}{8}[/tex] of the pizza
Given: Hernando ate [tex]\frac{2}{8}[/tex] of a pizza, number of friends is 6
First, let's find out what fraction of the pizza is left after Hernando ate his portion. Hernando ate [tex]\frac{2}{8}[/tex], which reduces to [tex]\frac{1}{4}[/tex]. Therefore, the remaining fraction of the pizza is:
[tex]1- \frac{1}{4} =\frac{4-1}{4} = \frac{3}{4}[/tex]
The remaining [tex]\frac{3}{4}[/tex] of the pizza is to be shared equally among his 6 friends. To find out how much pizza each friend gets, we divide the remaining fraction by the number of friends:
[tex]\frac{3}{4}[/tex] ÷ 6 [tex]=\frac{3}{4} \times \frac{1}{6} = \frac{1}{8}[/tex]
Each of Hernando's 6 friends gets [tex]\frac{1}{8}[/tex] of the pizza.
Using the quadratic formula to solve x2 = 5 – x, what are the values of x?
Answer:
x^2=5-x
x^2+x-5=0
x=-1± √(1)^2-4(1)(-5) /2(1)
-1± √21 /2
Step-by-step explanation:
Answer:
The answer will be A. -1± √21 /2
Step-by-step explanation:
I hope it helps
Luke is keeping track of the total number of hours he exercises. He started the summer having already put in 15 hours, and he then exercises 7 hours each week. The function to keep track of his exercise is f(x) = 7x + 15. What do the f(x) and x represent in Luke's situation?
f(x) is the total number of hours overall that he has worked out.
x would be the number of weeks he works out.
You would multiply x ( number f weeks he works out) by 7 and then add that to the hours he already worked out (15) which will give you the total hours (f(x)).
Answer:
In this case, x represents "week", because they problem says that he exercises 7 hour per week, being week an unknown number because we don't how much time Luke is gonna keep exercising. Si, 7x represents the total amount of hours per week after the first 15 hours.
Similarly, f(x) represents the total amount of hour from the beginning, before the first 15 hours. The difference between x and f(x) is that the first one represents hours after the 15 hours, and the second one represents the total amount of hours, including before the 15 hours.
It's important to notice that 15 is not multiplied by a variable, it's because those 15 hours are already achieve, we don't if those where monthly or weekly, but the fact that they already happened means that they can't change, that's why the don't have a variable.
Need help fast as soon as possible!!!
Answer:C 13/2
Step-by-step explanation: you do 13 x 0.5 equals 6.5, convert to a fratcion equals 13/2
Answer:
[tex]\frac{13}{2}[/tex]
Step-by-step explanation:
When you have a whole number, you gotta add a denominator, so just add 1 underneath:
[tex]\frac{13}{1}[/tex]
Then you have
[tex]\frac{13}{1}[/tex] ×[tex]\frac{1}{2}[/tex]
Multiply straight across and you get
[tex]\frac{13}{2}[/tex]
(3,0),(-11,-15) slope
Slope formula: y2-y1/x2-x1
Plug in: -15-0/-11-3 = -15/-14 = 15/14 = slope
For this case we have by definition, the slope of a line can be found by the following formula:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
Two points are needed through which the line passes.
According to the data we have:
[tex](x_ {1}, y_ {1}) :( 3,0)\\(x_ {2}, y_ {2}): (- 11, -15)[/tex]
Substituting we have:
[tex]m = \frac {-15-0} {- 11-3} = \frac {-15} {- 14} = \frac {15} {14}[/tex]
ANswer:
The slope is [tex]\frac {15} {14}[/tex]
Please someone help me
Answer:
The correct answer option is D. 5.
Step-by-step explanation:
We are given the following expression where 4 is to be divided by a fraction 1/5:
[tex] 4 [/tex] ÷ [tex]\frac{1}{5}[/tex]
This can also be written as:
[tex]\frac{4}{\frac{1}{5} }[/tex]
Now to find the quotient of this, we will take the reciprocal of the fraction in the denominator to change it into multiplication.
[tex]4 \times \frac{5}{1}[/tex]
Therefore, ignoring the 1 in denominator, we can simply multiply 4 by 5.
Answer:
Hi there!
The answer is last one: 5
Step-by-step explanation:
When ever you are dividing a number by a fraction you always flip the fraction and multiply it, another way of saying it is multiplying by its reciprocal.
Graph the function y = x3 + 3x2 – x – 3. Which lists all of the turning points of the graph?
Answer:
(-1, 0)
Step-by-step explanation:
Jim, please use the symbol " ^ " to indicate exponentiation:
y = x^3 + 3x^2 – x – 3. Thanks.
A "turning point" is a point on the graph of a function at which the derivative changes sign (e. g., from positive to negative or vice versa). To identify turning points, we differentiate the given function twice, set the second derivative equal to zero and identify the x-values at which the sign of the derivative changes.
Given y = x^3 + 3x^2 – x – 3,
dy/dx = 3x^2 + 6x - 1
d²y
------ = 6x + 6 and this is zero at x = -1.
dx²
We can easily show that the 2nd derivative changes sign at x = -1.
Thus, the only turning point here is (-1, [-1]³ + 3[-1]² - [-1] - 3), or (-1, 0).
Answer: (-2,3) and (0,-3)
Step-by-step explanation:
Hanna and Swathi walked several miles for a charity. Altogether they walked more than 14 miles. If Hanna walked 8 miles
then which represents s the number of miles Hanna could have walked?
Answer:
S>6
Step-by-step explanation:
Let us suppose the distance walked by Hanna and swati is represented by H and S.
And total distance travelled is D
D=H+S
D>14
H+S>14
Given H=8
8+S>14
S>6
Hence swati walked more than 6 miles
Which equation represents a line that passes through (4,1/3 ) and has a slope of 3/4?
y – = (x – 4)
y – = (x – 4)
y – = 4(x – 3/4)
y – 4 = (x – 1/3)
Answer:
y - 1/3 = 3/4(x - 4)
Step-by-step explanation:
We know that the general equation of a line is the following:
y - yo = m(x-xo), where 'm' represents the slope of the line, and (xo, yo) is any point that belongs to the line.
Then, the equation of the line that passes through (4, 1/3) and has a slope of 3/4 is: y - 1/3 = 3/4(x - 4)
For this case we have that by definition, the slope-intersection equation of a line is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut point with the y axis.
They tell us as data that:
[tex]m = \frac {3} {4}[/tex]
Now the equation is:
[tex]y = \frac {3} {4} x + b[/tex]
We substitute the point to find "b":
[tex](4, \frac {1} {3})[/tex]
[tex]\frac {1} {3} = \frac {3} {4} (4) + b[/tex]
[tex]b = \frac {1} {3} -3\\b = - \frac {8} {3}[/tex]
Finally the equation is:
[tex]y = \frac {3} {4}x - \frac {8} {3}[/tex]
In point-slope form the equation is:
[tex]y- \frac {1} {3} = \frac {3} {4} (x-4)[/tex]
Answer:
[tex]y = \frac {3} {4}x - \frac {8} {3}[/tex]
Perform the computation and write the result in scientific notation:
5.27 x 10 exponent 5 power
________________
8.7 x 10 exponent -5 power
Express your answer rounded correctly to the proper number of significant figures.
Answer:
6.06 x [tex]10^{9}[/tex]
Step-by-step explanation:
(5.25 x [tex]10^{5}[/tex] ) / (8.7 x [tex]10^{-5}[/tex] )
= (5.25 x [tex]10^{5}[/tex] ) x( [tex]10^{5}[/tex] )/ (8.7 )
= (5.25 x [tex]10^{5 + 5}[/tex] )/ (8.7 )
= 0.606 x [tex]10^{10}[/tex]
= 6.06 x [tex]10^{9}[/tex]
Which statements about the system are true? Check all that apply. y =1/3 x – 4 3y – x = –7 The system has one solution. The system consists of parallel lines. Both lines have the same slope. Both lines have the same y–intercept. The equations represent the same line. The lines intersect.
ANSWER
The system consists of parallel lines. Both lines have the same slope.
EXPLANATION.
The first equation is
[tex]y = \frac{1}{3} x - 4[/tex]
This equation is in the slope-intercept form.
The second equation is
[tex]3y - x = - 7[/tex]
We write this one too in slope-intercept form so that we can make comparison.
[tex] \implies \: y = \frac{1}{3} x - \frac{7}{3} [/tex]
We can see that both equations have slope
[tex]m = \frac{1}{3} [/tex]
This means the two lines are parallel.
The two lines have different y-intercepts.
Two parallel lines with different y-intercepts will never meet.
The lines will never intersect.
Answer:
The true statements are:
- The system consists of parallel lines
- Both lines have the same slope
Step-by-step explanation:
* Lets talk about the solution of the linear equations
- There are three types of the solutions of the system of linear equations
# If the two lines intersect each other, then there is one solution
- The equations are ax+ by = c , dx + ey = f
# If the two lines parallel to each other, then there is no solution
- The equations are ax+ by = c , ax + by = d in its simplest form ,
where a is the coefficient of x , b is the coefficient of y and
c , d are the numerical terms
# If the two lines coincide (over each other), then there are infinite
solutions
- The equations are ax+ by = c , ax + by = c in its simplest form, where
a is the coefficient of x , b is the coefficient of y and c is the
numerical term
* Lets solve the problem
∵ The system of equation is:
y = 1/3 x - 4 ⇒ (1)
3y - x = -7 ⇒ (2)
- Lets put equation (1) in the form of equation (2)
∵ y = 1/3 x - 4 ⇒ multiply both sides by 3
∴ 3y = x - 12 ⇒ subtract x from both sides
∴ 3y - x = -12
∴ Equation (1) is 3y - x = -12
∵ Equation (2) is 3y - x = -7
∵ The coefficients of x and y in the two equation are equal
∵ The numerical terms in the two equations are not equal
∴ The equations have no solution because their lines are parallel
∵ The parallel lines have same slope
* The true statements are
- The system consists of parallel lines
- Both lines have the same slope
Which of the following is the result of flipping the graph of the function shown
below over the line y - x?
Answer:
See attachment
Step-by-step explanation:
When the graph of the given function is flipped over the line [tex]y=x[/tex], the coordinates will swap.
The mapping for a reflection in the line [tex]y=x[/tex] is [tex](x,y)\to(y,x)[/tex].
We can observe that one portion of the graph is in the first quadrant [tex](x,y)[/tex]. When we flip this part we will get [tex](y,x)[/tex], which is still in the first quadrant.
Also, when we flip the portion of the graph in the second quadrant (-x,y), we will obtain (y,-x), which is standing for all coordinates in the fourth quadrant.
The image is shown in the attachment.
Lynne loaned $480 to a friend. The friend paid back the ammount borrowed plus 10% interest. what was the total amount the friend paid to lynne?
Answer:
$480+$48=$528
Step-by-step explanation:
his friend paid him $480 and 10% so,
=10/100*480
=1/10*480
=480/10
=$48
so,his friend paid him $480+$48=$528.
-9x -5+6=19 simplify
Answer:
[tex]{\huge \boxed{x=-2}[/tex]
Step-by-step explanation:
First you do is add and subtracting numbers from left to right.
-5+6=1
-9x+1=19
Then subtract by 1 from both sides of equation.
-9x+1-1=19-1
Simplify.
-9x=18
Divide by -9 from both sides of equation.
-9x/-9=18/-9
Simplify, to find the answer.
18÷-9=-2
x=-2 is the correct answer.
I hope this helps you, and have a wonderful day!
Answer:
x=-2
Step-by-step explanation:
-9x -5+6=19
Combine like terms
-9x +1 = 19
Subtract 1 from each side
-9x +1-1 = 19-1
-9x = 18
Divide by -9
-9x/-9 = 18/-9
x = -2
What are the coordinates of Z?
Answer:
The correct answer option is C. (0, c).
Step-by-step explanation:
We are given an isosceles trapezoid with the coordinates of three of its vertices and we are to find the coordinates of Z.
Z is a point on the middle of one of the sides of the trapezoid.
Since Z lies on the horizontal x axis, therefore its x coordinate is 0 while the y coordinate can be seen from the vertex exactly at its right which is c.
Z (0, c)
==============================================
Explanation:
Note how the point (a,0) mirrors over the y axis to land on (-a,0)
A similar action will happen as we go from te point (b,c) to point W (-b, c), due to this figure being isosoceles.
The x coordinate changes from positive to negative. The y coordinate stays the same.
The point Z is the midpoint of the upper segment which spans from (-b,c) to (b,c)
Apply the midpoint formula to find where Z is located.
Add up the x coordinates and divide by 2: x = (-b+b)/2 = 0/2 = 0
Add up the y coordinates and divide by 2: y = (c+c)/2 = 2c/2 = c
So the midpoint is located at (x,y) = (0, c) which is where point Z is located as well.
Side note: it might help to replace the letters a, b and c with actual values, just so the problem is more concrete.
What is the area of the rhombus shown below?
EG = 20
FD = 15
To find the area of a rhombus, multiply the two diagonals together then divide by 2.
Area = 20 *15 = 300 / 2 = 150 sq. units.
When Steve woke up. His temperature was 102 degrees F. Two hours later it was 3 degrees lower. What was his temperature then?
Answer:
if it was 102 when he woke
e up and lowered then it will be 99 degree fahrenheit then
Final answer:
Steve's temperature decreased by 3 degrees from the original 102 degrees F, which means his temperature two hours later was 99 degrees F.
Explanation:
The student's question involves a basic mathematical operation, specifically subtraction, used to determine a change in temperature over time. Steve originally has a temperature of 102 degrees Fahrenheit. After two hours, his temperature has decreased by 3 degrees.
To find the new temperature, we subtract the decrease from the original:
102 degrees F - 3 degrees F = 99 degrees F.
So, Steve's temperature two hours later would be 99 degrees Fahrenheit.
Given right angle abc, what is the value of tan(A)
Answer:
C
Step-by-step explanation:
tanA = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{BC}{AC}[/tex] = [tex]\frac{24}{10}[/tex] = [tex]\frac{12}{5}[/tex]
The container that holds the water for the football team is 1/2 full. after pouring out 5 gallons of water, it is 3/10 full. How many gallons can the container hold?
Answer:
25 gallons.
Step-by-step explanation:
The container that holds the water for the football team is 1/2 full.
After pouring out 5 gallons of water, it is 3/10 full.
The proportion that was poured out is [tex]\frac{1}{2}[/tex] - [tex]\frac{3}{10}[/tex] = [tex]\frac{2}{10}[/tex] = [tex]\frac{1}{5}[/tex]
[tex]\frac{1}{5}[/tex] of the water in the container is equal to 5 gallons
The container therefore holds: 1 × 5 ÷ [tex]\frac{1}{5}[/tex] = 5 × 5 = 25 gallons.
Final answer:
The total capacity of the container is calculated to be 25 gallons, found by using the information that 1/2 to 3/10 of the capacity equals a 5 gallon difference.
Explanation:
We have been given that the container is initially 1/2 full and becomes 3/10 full after pouring out 5 gallons of water.
To find out the total capacity of the container, we can set up a proportion where the difference between the two fractions (1/2 and 3/10) represents the 5 gallons removed.
First, we find a common denominator for the two fractions, which is 10. Now we can say:
1/2 equals 5/10After removing 5 gallons, the container is 3/10 fullThe difference between 5/10 and 3/10 is 2/10, which equates to the 5 gallons poured out. Thus, 2/10 of the container's capacity is 5 gallons, and we can find the full capacity (10/10) by multiplying the 5 gallons by 5 (since 2 × 5=10).
So, the container's total capacity is 5 gallons × 5 = 25 gallons.