Answer:
[tex]\displaystyle about\:8\:units[/tex]
Step-by-step explanation:
Use the Distance Formula:
[tex]\displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = D \\ \\ \sqrt{[6 - 1]^2 + [-7 + 1]^2} = \sqrt{5^2 + [-6]^2} = \sqrt{25 + 36} = \sqrt{61} ≈ 7,810249676 ≈ 8[/tex]
Since we are talking about distance, we ONLY want the NON-NEGATIVE root.
I am joyous to assist you anytime.
A group of mountain climbers begin a expedition with 250 pounds of food. They plan to eat a total of 12 pounds of food per day . Write and solve a linear equation to find the number of days their food will last
Answer:
The equation representing total food consumption in [tex]x[/tex] days can be given as:
[tex]y=12x[/tex]
where [tex]y[/tex] represents total food taken which is =250 pounds and [tex]x[/tex] represnts the number of days the food will last.
The food will last for [tex]20\frac{5}{6}[/tex] days.
Step-by-step explanation:
Total pounds of food taken at the beginning = 250 pounds
Food consumed per day = 12 pounds
Let the total food at the beginning be = [tex]y[/tex] pounds
Let number of days the food will last be = [tex]x[/tex] days
Using unitary method to find the food consumed in [tex]x[/tex] days.
If in 1 day food consumed = 12 pounds
Then, in [tex]x[/tex] days food consumption = [tex]12\times x = 12x[/tex] pounds
So,the equation representing total food consumption in [tex]x[/tex] days can be given as:
[tex]y=12x[/tex]
Total food taken =250 pounds
Plugging in [tex]y=250[/tex] in the equation:
[tex]250=12x[/tex]
Solving for [tex]x[/tex]
Dividing both sides by 12.
[tex]\frac{250}{12}=\frac{12x}{12}[/tex]
[tex]\frac{250}{12}=x[/tex]
Simplifying fractions.
[tex]\frac{125}{6}=x[/tex]
Converting fraction to mixed number by writing quotient as whole number, remainder as numerator and divisor as denominator.
∴ [tex]x=20\frac{5}{6}[/tex] days.
Thus, the food will last for [tex]20\frac{5}{6}[/tex] days.
What is the value of e^ln7 x1
7e
7x
7
Answer:
7x
Step-by-step explanation:
Assuming your expression is :
[tex]e^{\ln 7x}[/tex]
Then we simplify as follows
[tex]e^{\ln 7x}=e^{\ln x+\ln 7}[/tex] since [tex]\ln A+\ln B=\ln AB[/tex]
[tex]\implies e^{\ln 7x}=e^{\ln x}\times e^{\ln 7}[/tex] since [tex]a^{m+n}=a^m\times a^n[/tex]
[tex]\implies e^{\ln 7x}=x\times7[/tex] since [tex]e^{\ln a}=a[/tex]
[tex]\implies e^{\ln 7x}=7x[/tex]
m=7/4 (3,-4) point slope form
Answer:
y+4=7/4(x-3)
Step-by-step explanation:
y-y1=m(x-x1)
y-(-4)=7/4(x-3)
y+4=7/4(x-3)
Is 4 and 4 perpendicular
Answer:
No.
Step-by-step explanation:
Because perpendicular means negative reciprocal of the slope. So 4 and -1/4 are perpendicular.
the square root of 52 is between which two consecutive intergers?
a) 26 and 27
b) 7 and 8
c) 25 and 26
d) 8 and 9
Answer: 7 and 8
Step-by-step explanation:
The square root of 7 is 49 and the square root of 8 is 64
52 is in between the 2 consecutive integers 7 and 8
Answer: b) 7 and 8
Step-by-step explanation:
The formula for calculating the square root of non perfect square is given as :
square root of non perfect square = square root of the nearest lower perfect square + (difference between the number and the perfect square)/ 2x the perfect square.
To find the square root of 52.
The nearest lower perfect square to 52 is 49 , applying the formula , we have:
[tex]\sqrt{52}[/tex] = [tex]\sqrt{49}[/tex] - [tex]\frac{52-49}{2\sqrt{49}}[/tex]
[tex]\sqrt{52}[/tex] = 7 + [tex]\frac{3}{2(7)}[/tex]
[tex]\sqrt{52}[/tex] = 7 + [tex]\frac{3}{14}[/tex]
This shows clearly that [tex]\sqrt{52}[/tex] is between the integer 7 and 8
Consider a circle that has a circumference of 28/3.14 centimeters. What is the area of this circle? Answer fast plz also can you show work???
Answer:
[tex]A=6.33\ cm^2[/tex]
Step-by-step explanation:
step 1
Find the radius of the circle
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]C=\frac{28}{3.14}\ cm[/tex]
[tex]\pi=3.14[/tex]
substitute the values
[tex]\frac{28}{3.14}=2(3.14)r[/tex]
[tex]r=\frac{28}{19.7192}\ cm[/tex]
[tex]r=1.42\ cm[/tex]
step 2
Find the area of the circle
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
substitute the values
[tex]A=(3.14)(1.42)^{2}[/tex]
[tex]A=6.33\ cm^2[/tex]
if w = -2 and V = -8 which of the following Expressions shown the values correctly substituted and for the valuables in the expression w^2 - v + 1
1. -2^2 - (-8) + 1
2. -2^2 - 8 + 1
3. (-2)^2 - (8) + 1
4. (-2)^2 - (-8) + 1
Answer:
D) (-2)^2-(-8)+1
Step-by-step explanation:
Answer: 4
Step-by-step explanation:
The ages of three friends are consecutive integers. If the sum of the three
friends' ages is 45, which equation below can be used to determine the age, x,
of the youngest friend?
Answer:
Step-by-step explanation:
Let the consecutive integers be (x - 1), x, (x + x)
x - 1 + x + x + 1 = 45
3x = 45 ---------> this is the equation
x = 45/3
x = 15
The ages are 14,15,16
Answer:
Step-by-step explanation:
consecutive integers means 1 right after the other....with x being the youngest, then x + 1 being the second friend, and x + 2 being the third friend.
so ur equation would be : x + x + 1 + x + 2 = 45......but since I cant see ur answer choices, it could also be : 3x + 3 = 45
The equation 5x - 7(x-1) = ax+b has exactly one solution.
Answer:
a = -2 and b = 7
Step-by-step explanation:
We need to solve for the value of "a" and "b".
We need to distribute and make the left side of the equation same form as the right side of the equation and match the coefficients, simple.
We will use the distributive property shown below to expand the left side and simplify.
Distributive Property: a(b-c) = ab - ac
Now, simplifying left hand side:
5x - 7(x - 1)
= 5x -7(x) -7(-1)
= 5x -7x +7
= -2x + 7
The right hand side is "ax + b".
If we match left-hand side and right-hand side, we see that:
a = -2
and
b = 7
THese are the only solution.
14. © MP.1 Make Sense and Persevere
Hodi is building a birdhouse. Each of the
four walls of the birdhouse needs to be
5.5 inches long. Hodi has a piece of
board that is 24.5 inches long. Is the
board long enough to be cut into the four
walls of the birdhouse? Estimate using
compatible numbers.
Answer:
This board of 24.5 inches long is not enough to be cut into the four walls of the bird house.
Step-by-step explanation:
Hodi is building a birdhouse. Each of the four walls of the birdhouse needs to be 5.5 inches long.
So, to get four 5.5 inches long walls we need to have (5.5 × 4) = 22 inches ling board from which four equal 5.5 inches board can be made.
Now, Hodi has a piece of a board that is 24.5 inches long.
Therefore, this board is not enough to be cut into the four walls of the birdhouse. (Answer)
three tanks are capable of holding 108 litres, 168 litres and 180 litres of milk. determine the capacity of the greatest vessel which can be used to fill each one of them an exact number of time.
A vessel of 7,560 liters
Step-by-step explanation:
This means finding the Least Common Multiple for;
108 168 180
We begin by finding the multiples of each number;
Multiples of 108:
108, 216, 324, 432, 540, 648, 756, 864, 972, 1080, 1188, 1296, 1404, 1512, 1620, 1728, 1836, 1944, 2052, 2160, 2268, 2376, 2484, 2592, 2700, 2808, 2916, 3024, 3132, 3240, 3348, 3456, 3564, 3672, 3780, 3888, 3996, 4104, 4212, 4320, 4428, 4536, 4644, 4752, 4860, 4968, 5076, 5184, 5292, 5400, 5508, 5616, 5724, 5832, 5940, 6048, 6156, 6264, 6372, 6480, 6588, 6696, 6804, 6912, 7020, 7128, 7236, 7344, 7452, 7560, 7668, 7776
Multiples of 168:
168, 336, 504, 672, 840, 1008, 1176, 1344, 1512, 1680, 1848, 2016, 2184, 2352, 2520, 2688, 2856, 3024, 3192, 3360, 3528, 3696, 3864, 4032, 4200, 4368, 4536, 4704, 4872, 5040, 5208, 5376, 5544, 5712, 5880, 6048, 6216, 6384, 6552, 6720, 6888, 7056, 7224, 7392, 7560, 7728, 7896
Multiples of 180:
180, 360, 540, 720, 900, 1080, 1260, 1440, 1620, 1800, 1980, 2160, 2340, 2520, 2700, 2880, 3060, 3240, 3420, 3600, 3780, 3960, 4140, 4320, 4500, 4680, 4860, 5040, 5220, 5400, 5580, 5760, 5940, 6120, 6300, 6480, 6660, 6840, 7020, 7200, 7380, 7560, 7740, 7920
The Least Common Multiple for the 3 number is;
= 7560
Therefore a vessel of 7,560 liters fills each one of them an exact number of times with no remainder.
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Compare the line passing through the points (-2,-9) and (4, 6) with the line given by the equation
y = 2/5x -4.
A) they have the same slope
B) they have the same x-intercept
C) the two lines are perpendicular
D) they have the same Y-intercept
For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It is the slope of the line
b: It is the cut-off point with the y axis
We have the following points:
[tex](x_ {1}, y_ {1}) :( 4,6)\\(x_ {2}, y_ {2}): (- 2, -9)[/tex]
We can find the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-9-6} {- 2-4} = \frac {-15} {- 6} = \frac {5} {2}[/tex]
Thus, the equation is of the form:
[tex]y = \frac {5} {2} x + b[/tex]
We substitute one of the points and find "b":
[tex]6 = \frac {5} {2} (4) + b\\6 = 10 + b\\6-10 = b\\b = -4[/tex]
Finally, the equation is:
[tex]y = \frac {5} {2} x-4[/tex]
Thus, it is observed that the lines have the same y-intercept
Answer:
Option D
Which number(s) from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, if any, will solve this equation? I PROMISE TO MARK BARINLEST + EXTRA POINTS!!!!!!!!!!!!
2x + 3 = 5x - 3
Answer:
2
Step-by-step explanation:2x + 3 = 5x - 3
Move x to one side:
[tex]2x-2x+3=5x-2x-3\\3=3x-3[/tex]
Remove the -3:
[tex]3x-3(+3)=(3+3)[/tex]
[tex]3x=6[/tex]
Remove the 6 to get x by itself:
[tex]\frac{3x}{3} =\frac{6}{3} \\x=2[/tex]
The number 2 from the number set would solve the equation.
Checking the Answer:2(2) + 3 = 5(2) - 3
4 + 3 = 10 - 3
7 = 7
The statement is true.
An equation is formed of two equal expressions. The number(s) from the set that will satisfy the given equation is 2.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation can be simplified as shown below,
2x + 3 = 5x - 3
Subtract 2x from both sides of the equation,
2x + 3 - 2x = 5x - 3 - 2x
3 = 5x - 3 - 2x
Add 3 on both sides of the equation,
3 + 3 = 5x - 3 - 2x + 3
6 = 3x
3x = 6
Divide both the sides of the equation by 3,
3x/3 = 6/3
x = 2
Hence, the number(s) from the set that will satisfy the given equation is 2.
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10 POINTS!!
Point p is chosen at random on KN. Find the probability that p is on LM.
Answer:
[tex]\frac{4}{11}[/tex]
Step-by-step explanation:
The total length of KN is 11 units and the length of LM is 4 units. This means that the probability would be [tex]\frac{4}{11}[/tex]
Answer : The probability that p on LM is, [tex]\frac{4}{11}[/tex]
Step-by-step explanation :
Probability : It is defined as the extent to which an event is likely to occur. That means, it is measured by the ratio of the favorable outcomes to the total number of possible outcomes.
[tex]\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of favorable outcomes}}[/tex]
Favorable outcomes on line KN are, 2, 4, 5
Favorable outcomes on line LM is, 4
Number of favorable outcomes = 4
Total number of outcomes = 2 + 4 + 5 = 11
[tex]\text{Probability}=\frac{\text{Number of favorable outcomes for a multiple of 3}}{\text{Total number of favorable outcomes}}[/tex]
[tex]\text{Probability}=\frac{4}{11}[/tex]
Therefore, the probability that p on LM is, [tex]\frac{4}{11}[/tex]
Which BEST describes the system of equations?
y - 2x = 4
y + 2 = 2x
Consistent
Inconsistent
Consistent and Dependent
Consistent and independent
Answer:
Inconsistent
Step-by-step explanation:
Given system of equations.
A) [tex]y-2x=4[/tex]
B) [tex]y+2=2x[/tex]
We will solve the system of equations to check the solutions and tell whether the system is consistent or inconsistent
Rearranging equation A, to solve for [tex]y[/tex] in terms of [tex]x[/tex]
Adding both sides by [tex]2x[/tex]
[tex]y-2x+2x=4+2x[/tex]
[tex]y=4+2x[/tex]
Substituting value of [tex]y[/tex] we got from A into equation B.
[tex]4+2x+2=2x[/tex]
Simplifying.
[tex]2x+6=2x[/tex]
Subtracting both sides by [tex]2x[/tex]
[tex]2x-2x+6=2x-2x[/tex]
[tex]6=0[/tex]
This is never true. So, we can say the system of equation has no solutions as the equations of the lines given are parallel.
Any system of equation with no solutions is termed as inconsistent.
Answer:
D) Consistent and Independent
Step-by-step explanation:
I did it on USA test prep.
A city allocates 31.84% of its budget for schools. If the schools receive $17,467,472 this year, what is the city’s total budget to nearest dollar?
Answer:
The city’s total budget is [tex]\$54,860,151[/tex]
Step-by-step explanation:
we know that
31.84% of the city's total budget represent $17,467,472
so
using proportion
Find out what is the city’s total budget (100% percentage)
[tex]\frac{\$17,467,472}{31.84\%}=\frac{x}{100\%}\\\\x=\$17,467,472(100)/31.84\\\\x=\$54,860,151[/tex]
How much less would a 23-year-old female pay for a $25,000 policy of 20 year life insurance (@ $2.90 per $1000) than straight life (@ $15.78 per $1000)?
Answer:
The female would pay $322.00 less for a policy of $25,000
Step-by-step explanation:
Since we have given that
Amount for policy = $25000
If she opt for 20 year life insurance at $2.90 per $1000.
so, her amount of premium becomes
[tex]25000\times \frac{2.9}{1000}[/tex]
=$72.50
If she opt for straight life insurance at $15.78 per $1000,
Then, her amount of premium becomes
[tex]25000 \times \frac{15.78}{1000}[/tex]
= $394.50
Difference between them is given by
$394.50-$72.5 = $322.00
Answer:
The answer to this question is $322.
Step-by-step explanation:
From the question, we recall the following
23-year-old female pay for a $25,000 policy less policy of 20 year life insurance.
The first step is to calculate the policy of 20 year life insurance
The number of thousands on 2500 is, 25000/1000=25
25*2.9 = 72.5
The next step is to get the straight life
Thus,
25×15.78 = 394.5
Now,
How much less would the 23 year old pay
394.5−72.5 = $322
Study the graph below.
Coordinate plane with x-axis labeled as quantity A and the y-axis labeled as quantity B. Graph contains a line that passes through the following points: (0, 0), (3, 4) and (6, 8).
Describe the functional relationship between the two quantities in the graph.
Answer:
[tex]B=\frac{4}{3}A[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In this problem we have a proportional relationship because the line passes through the origin (0,0)
Find the value of k
[tex]k=\frac{B}{A}[/tex]
take the point (3,4)
A=3,B=4
substitute
[tex]k=\frac{4}{3}[/tex]
The equation of the line is
[tex]B=\frac{4}{3}A[/tex]
The measurement of the side of a RV is 469 inches the actual length is 480 inches what is the percent error
Answer:
Step-by-step explanation:
error in measurement = 480 - 469 = 11 inches
Percent error = error *100/actual length
= 11 * 100 /480 = 2.9%
Write point-slope form of the equation that represents the line that passes through the point (−3, 9) and has a slope of 5.
Answer:
y-9=5(x+3)
Step-by-step explanation:
y-y1=m(x-x1)
y-9=5(x-(-3))
y-9=5(x+3)
WILL GIVE BRAINLIST
Fill in the blank with a number to make the expression a perfect square.
w² - 6w + ___
Answer:
9 should be added to the expression to make it a perfect square
Step-by-step explanation:
Given expression:
[tex]w^2-6w+_-[/tex]
To fill in the missing term such that the expression becomes a perfect square.
Solution:
In order to make the expression a perfect square we will use completing the square method.
We have : [tex]w^2-6w[/tex]
By complete the square method we will add the square of the quotient of the co-efficient of the middle term which is [tex]-6w[/tex] and 2.
The co-efficient of middle term = -6
Thus the number to be added will be = [tex](\frac{-6}{2})^2=(-3)^2=9[/tex]
Thus, on adding 9 the expression will become:
[tex]w^2-6w+9[/tex] which is a perfect square of the binomial [tex](w-3)[/tex]
This can be shown as:
[tex](w-3)^2=w^2-6w+9[/tex]
Thus, we add 9 to the expression to make it a perfect square.
Answer:
9
Step-by-step explanation:
Given: [tex]w^{2} -6w+[/tex]
Finding the number to make expression a perfect square.
From the expression we can see that coefficient of variable is 1 and -6.
Now, lets take a= 1 and b= -6 and finding c .
∴ c= [tex]\frac{b^{2} }{4a}[/tex]
Subtituting the value of a and b.
⇒ c= [tex]\frac{-6^{2} }{4\times 1} = \frac{36}{4}[/tex] (∵ [tex]-6\times -6= 36[/tex])
∴ c= 9
Next putting the value in the expression.
[tex]w^{2} -6w+9[/tex]
= [tex](w-3)(w-3)[/tex]
= [tex](w-3)^{2}[/tex]
Hence, 9 is a number to make the expression a perfect square.
Write the equation of the line that passes through the point (3, -5) and is perpendicular to the line x = 4.
Answer:
3r-5r
Step-by-step explanation:
-4 ^ 3 * 2 / 8 * 20 + 125
What is the area of the following circle?
Either enter an exact answer in terms of π (pi) or use 3.14 and enter your answer as a decimal.
Answer:
Area of the circle is following:
[tex]a = \pi \: r {}^{2} [/tex]
So there is radius=1
Putting it into formula:
[tex]a = \pi \: 1 {}^{2} \\ a = \pi \\ a = 3.14[/tex]
So the answer is
[tex]3.14 \: units {}^{2} [/tex]
Good luck!
Intelligent Muslim,
From Uzbekistan.
Two cars leave towns
400
kilometers apart at the same time and travel toward each other. One car's rate is
12
kilometers per hour less than the other's. If they meet in
2
hours, what is the rate of the slower car?
The speed of slower car is 94 kilometers per hour.
Step-by-step explanation:
Given,
Total distance covered by both cars = 400 km
Time period = 2 hours
Let,
Speed of one car = x
Speed of slower car = x-12
Combined speed = [tex]x+(x-12)=x+x-12=2x-12[/tex]
Distance = Speed*Time
[tex]400=(2x-12)*2\\400=4x-24\\400+24=4x\\424=4x\\4x=424[/tex]
Dividing both sides by 4
[tex]\frac{4x}{4}=\frac{424}{4}\\x=106[/tex]
Speed of slower car = x-12 = 106-12 = 94 km/h
The speed of slower car is 94 kilometers per hour.
Keywords: distance, speed, time
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A birdhouse has a shadow that is 12 feet long.
Jin is 5 feet tall, and he is standing next to the birdhouse.
Jin has a shadow that is 3 feet long. What is the height of the birdhouse in feet ?
Answer: 5 feet tall
Step-by-step explanation:
because he is beside the bird house he is 5 feet tall
The birdhouse's height is 20 feet, calculated using the proportion: [tex]\( \frac{h}{12} = \frac{5}{3} \).[/tex]
We can solve this problem using proportions.
Let [tex]\( h \)[/tex] be the height of the birdhouse.
According to the given information, the ratio of Jin's height to his shadow length is the same as the ratio of the birdhouse's height to its shadow length:
[tex]\[ \frac{h}{12} = \frac{5}{3} \][/tex]
Now, cross-multiply to solve for [tex]\( h \):[/tex]
[tex]\[ 3h = 5 \times 12 \][/tex]
[tex]\[ 3h = 60 \][/tex]
[tex]\[ h = \frac{60}{3} \][/tex]
[tex]\[ h = 20 \][/tex]
So, the height of the birdhouse is 20 feet.
Theatre are of a square park is 400sqm. Calcuate the length of side of park
Answer:
The Length of side of park is 20 meter.
Step-by-step explanation:
Given:
Shape of a Park is SQUARE
Area of a square park = 400 sqm
To Find:
The length of side of park = side = ?
Solution:
We know For a SQUARE
All the sides are equal
And Area of a square is given as
[tex]\textrm{Area of Square Park}= (Side)^{2} \\[/tex]
Substituting the given values we get
[tex]400=(side)^{2} \\\\\textrm{Square rooting we get}\\\\side=\sqrt{400} \\\\\therefore side = 20\ meter[/tex]
The Length of side of park is 20 meter.
As the pastry chef in a restaurant, you have a recipe that uses 4 cups of flour to make 3 dozen cookies. You want to make 15 dozen cookies. How many cups of flour will you need
Answer:
you will need 4cups of flour
Mr. Snow bought 90 grams of Christmas candy for each of his 14 grandchildren. How many total kilograms of candy did he buy?
Answer:
1.26 kg.
Step-by-step explanation:
We have been given that Mr. Snow bought 90 grams of Christmas candy for each of his 14 grandchildren. We are asked to find the amount of candy bought by Mr. Snow in kilograms.
First of all, we will find the amount of candy in grams by multiplying 90 grams by 14 as:
[tex]\text{Amount of candy bought in grams}=14\times 90[/tex]
[tex]\text{Amount of candy bought in grams}=1260[/tex]
We know that 1 kilogram is equal to 1000 grams. To convert 1260 grams into kg, we will divide 1260 by 1000 as:
[tex]\text{Amount of candy bought in kilograms}=\frac{1260}{1000}[/tex]
[tex]\text{Amount of candy bought in kilograms}=1.26[/tex]
Therefore, Mr. Snow bought 1.26 kilograms of candy.
the sum of 6c- 5c and the opposite of 6c
Answer:
[tex]-5c[/tex]
Step-by-step explanation:
To find: The sum of [tex]6c-5c[/tex] and opposite of [tex]6c[/tex]
Opposite of [tex]6c[/tex] means taking the opposite sign.
[tex]6c[/tex] is positive. So, opposite sign is [tex]-6c[/tex].
Therefore, the addition is given as:
[tex]=6c-5c+(-6c)[/tex]
Opening the parenthesis, we get:
[tex]6c-5c-6c[/tex]
Now, as per PEDMAS rule, we subtract [tex]6c\ and\ 5c[/tex], we get
[tex]6c-5c=(6-5)c=1c[/tex]
Now, we are left with [tex]1c-6c[/tex]
Subtracting a bigger number from a smaller number will give a negative answer.
So, [tex]1c-6c=(1-6)c=-5c[/tex]
Therefore, the final answer is [tex]-5c[/tex]