Answers
we have the equation
[tex]P(t)=319(2)^{(\frac{t}{3})}[/tex]For P(t)=2,552
substitute in the given equation
[tex]2,552=319(2)^{(\frac{t}{3})}[/tex]solve for t
[tex]\begin{gathered} 2,552=319(2)^{(\frac{t}{3})} \\ \frac{2,552}{319}=(2)^{(\frac{t}{3})} \end{gathered}[/tex]Apply log both sides
[tex]\begin{gathered} \log \lbrack\frac{2,552}{319}\rbrack=\log \lbrack(2)^{(\frac{t}{3})}\rbrack \\ \log \lbrack\frac{2,552}{319}\rbrack=\frac{t}{3}\cdot\log (2) \end{gathered}[/tex]t=9 yearsthe answer is 9 years from the time of introductionRelated Questions
Convert 57•F to degrees Celsius. If necessary, round your answer to the nearest tenth of a degree. Here are the formulas.C=5/9 (F-32)F= 9/5 C+32
Answers
ANSWER
[tex]13.9°C[/tex]EXPLANATION
We want to convert 57°F to degrees Celsius.
To do this, apply the formula:
[tex]C=\frac{5}{9}(F-32)[/tex]where F = temperature in Fahrenheit
Therefore, 57°F to degrees Celsius is:
[tex]\begin{gathered} C=\frac{5}{9}(57-32) \\ \\ C=\frac{5}{9}*25 \\ \\ C=13.9°C \end{gathered}[/tex]That is the answer.
Eric needs to manufacture a turntable with a circumference of `140pi` centimeters. If the allowed error tolerance in the circumference is `+-5` centimeters, how close to the ideal radius must he control the radius of the turntable?
A. `10/pi`
B. `2/pi`
C. 5/(2pi)`
D. `5/(4pi)`
Answer: is C. `5/(2pi)`
Answers
The correct option is C 5/(2π) . The ideal radius must he control the radius of the turntable will be 5/(2π) .
What is meant by circumference?circle's circumference 22 inches around make up the circle. Periphery from the center to the sphere's circumference: 2: an object or figure's external boundary or surface The circumference, which in geometry refers to a circle or ellipse's perimeter, is derived from the Latin circumferens, which means "carrying around." In other words, the circumference would be the length of the circle's arc if it were opened out and straightened out to a line segment. Any great circle's circumference, or the distance between any two planes that cross a sphere's center, is measured in meters. Any large circle that traverses a pole-designated point is known as a meridian. The shortest path between any two locations on a sphere is referred to as a geodesic.
To know more about circumference ,visit:
brainly.com/question/28757341
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solve the value of the variable7(3x-4)=6x-4+3x+12
Answers
7(3x-4) = 6x -4 +3x +12
Distributing:
7(3x) -7(4) = 6x -4 +3x +12
21x - 28 = 6x -4 +3x +12
Combining similar terms:
21x - 28 = (6x + 3x) + (-4 +12)
21x - 28 = 9x + 8
9x is adding on the right, then it will subtract on the left
28 is subtracting on the left, then it will add on the right
21x - 9x = 8 + 28
12x = 36
12 is multiplying on the left, then it will divide on the right
x = 36/12
x = 3
Which rule describes the transformation used tocreate GHI from DEF?A. (x,y) → (-y, x)B. (x,y) → (-X, -y)C. (x,y) → (x, -y)D. (x,y) → (y, -x)
Answers
Explanation:
We can see that the points are mapped as:
[tex]\begin{gathered} G(5,-1)\rightarrow D(-5,1) \\ H(5,2)\rightarrow E(-5,-2) \\ I(-1,2)\rightarrow F(1,-2) \end{gathered}[/tex]Therefore the coordinates of each point change to its opposite.
Answer:
The rule is:
B. (x, y) → (-x, -y)
the sophomores are planning a homecoming dance they want to hire a band band a charges $600 to play for the night Band B charges $375 plus $10 for each ticket sold at the sophomore sold 30 tickets which band Chargers higher
Answers
• Charges $600 to play for the night.
Notice that this cost is to play the whole night, it's a fixed cost.
[tex]A=600[/tex]Band B.• Charges $375 plus $10 for each ticket sold.
,• The sophomore sold 30 tickets.
This band has a fixed cost plus a fee of $10, which is $300 more because they sold 30 tickets.
So, the cost of this band would be
[tex]B=350+10(30)=350+300=650[/tex]Therefore, Band B will charge more than Band A.Cual es el resultado de (5)⁶
Answers
Answer:
15625
Step-by-step explanation:
5x5x5x5x5x5=15625
5 times itself 6 times
An open box is made from a 30cm by 40cm piece of tin by cutting
Answers
s represents the square
[tex]\begin{gathered} s_{1,\: 2}=\frac{-\left(-35\right)\pm\sqrt{\left(-35\right)^2-4\cdot\:1\cdot\:34}}{2\cdot\:1} \\ s_{1,\: 2}=\frac{-\left(-35\right)\pm\:33}{2\cdot\:1} \\ s_1=\frac{-\left(-35\right)+33}{2\cdot\:1}=\frac{35+33}{2}=\frac{68}{2}=34 \\ s_2=\frac{-\left(-35\right)-33}{2\cdot\:1}=\frac{35-33}{2}=\frac{2}{2}=1 \end{gathered}[/tex]The length of the sides of the square is 1 cm
Please help me quickly I don’t need the explanation I just need the answer I’m sorry I just need a fast
Answers
Notice that the area is equivalent to the area of the complete rectangle minus the area of the 3km x 4km rectangle.
[tex]A=TA-AS\text{.}[/tex]Now, the area of a rectangle is given by the following formula:
[tex]A=\text{width}\cdot\text{lenght.}[/tex]Therefore:
[tex]A=9km\cdot16km-3km\cdot4km\text{.}[/tex]Simplifying the above result, we get:
[tex]A=(144-12)km^2=132km^2.[/tex]Answer:
[tex]132km^2.[/tex]Find the exact value of the expression:4^log16^(7)A) ✓7B) 2✓3C) 8D) 49
Answers
Answer:
A) ✓7
Explanation:
Given the expression:
[tex]4^{\log _{16}7}[/tex]First, we can rewrite 4 as a root of 16.
[tex]=16^{\frac{1}{2}\log _{16}7}[/tex]Next, by the power law of logarithm:
[tex]a\log x=\log x^a\implies\frac{1}{2}\log _{16}7=\log _{16}7^{\frac{1}{2}}[/tex]Thus, our given expression becomes:
[tex]=16^{\log _{16}\sqrt{7}}[/tex]Using the logarithm property below:
[tex]\begin{gathered} x^{\log _xa}=a \\ \implies16^{\log _{16}\sqrt[]{7}}=\sqrt[]{7} \end{gathered}[/tex]The exact value of the expression is ✓7.
Option A is correct.
I need help just a understanding. And show how to get the answer.
Answers
An angle is formed when two lines meet. The angle is named with the lines that forms it. Looking at the diagram, the angle 2 is formed at B by lines CB and DB. The correct name for angle 2 is angle CBD
The last option is correct
Dilate the figure by the scale factor. Then enterthe new coordinates.A(-1,1)B(4,0)K=5A'( [?],[])B'( 1 )C'([ ],[]).C(1,-3)EnterAnswer
Answers
A dilation is a proportional stretch or shrink of an image based on a scale factor. It is represented by:
[tex](x,y)\rightarrow(K\cdot x,\text{ K}\cdot y)[/tex]Then, for the figure on the question tab and scale factor of 5:
[tex]A(-1,1)\rightarrow A^{\prime}(-1\cdot5,1\cdot5)=A^{\prime}(-5,\text{ 5)}[/tex][tex]B(4,0)\rightarrow B^{\prime}(4\cdot5,0\cdot5)=B^{\prime}(20,0)[/tex][tex]C(1,-3)\rightarrow C^{\prime}(1\cdot5,-3\cdot5)=C^{\prime}(5,-15)[/tex]For her phone service, Lucy pays a monthly fee of $15, and she pays an additional $0.05 per minute of use. The least she has been charged in a month is$84.75What are the possible numbers of minutes she has used her phone in a month?Use m for the number of minutes, and solve your inequality for m.
Answers
m ≥ 1395 minutes
Explanation:Monthly fee = $15
fee paid per minute of use = $0.05
let the number of minutes she used = m
The least amount she has been charged = $84.75
least is written as ≥ $84.75
The equation:
Monthly fee + fee per minute(number of minutes) = The total charge
The equal sign changed below since the question mentioned the least amount
$15 + 0.05(m) ≥ $84.75
15 + 0.05m ≥ 84.75
To get the possible number of minutes, we will solve for m:
15 + 0.05m ≥ 84.75
subtract 15 from both sides:
0.05m ≥ 84.75 - 15
0.05m ≥ 69.75
divide both sides by 0.05:
m ≥ 69.75/0.05
m ≥ 1395 minutes
The possible number of minutes she has used her phone in a month is at least 1395 minutes
Why aren't there infinitely many semi-regular tessellations?
Answers
Regular tessellations use identical regular polygons to fill the plane. The polygons must line up vertex to vertex, edge to edge, leaving no gaps.
Semi-regular tessellations have two properties:
• They are formed by two or more types of regular polygon, each with the same side length
,• Each vertex has the same pattern of polygons around it.
There are 8 semi-regular tessellations in total. We know each is correct because again, the internal angle of these shapes add up to 360.
For example, for triangles and squares, 60 × 3 + 90 × 2 = 360.
(credited)
Fibonacci, Pythagoras and Descartes went out for breakfast. The total bill was $38.50. The tax rate was 7% and they left a 20% tip. Determine the total bill. Round to the nearest hundredth.so how much will each person pay if the bill was equally divided?
Answers
Given:
• Total bill = $38.50
,• Tax rate = 7% = 0.07
,• Tip = 20% = 0.20
Let's find the total bill after tax and tip.
Now, to find the total bill we have:
Total bill = bill + tax amount + tip amount
Where:
[tex]\begin{gathered} \text{ tax amount = 0.07}\times38.50=2.695 \\ \\ Tip\text{ amount = 0.20 }\times38.50=7.7 \end{gathered}[/tex]The tax amount is $2.695
The tip amount is $7.70
Now, to find the total bill, we have:
Total bill = $38.50 + $2.695 + $7.7 = $48.895 ≈ $48.90
Therefore, the total bill rounded to the nearest hundredth is $48.90
Part B.
To find the amount each person will pay if the bill was equally divided, let's divide the total bill by the number of people.
Where:
Number of people = 3
Hence, we have:
[tex]\frac{48.90}{3}=\text{ 16.30}[/tex]Therefore, the amount each person will pay is $16.30
ANSWER:
(a). $48.90
(b). $16.30
given the parent function f(x)=ab^x how could changing from a 2 to -2 cause f(x) to change? use words like "increasing" "decreasing" "positive" "negative" "domain" and "range" to describe the similarities and differences in the graph
Answers
Here, we want to get the response of the given function with respect to the change in the value of the leading coefficient
As we can see from the question, what we have is an example of an exponential function
Generally, with exponential function with a positive value for a, as the value of x moves closer to negative infinity, we have that the value of f(x) moves closer to 0. What this mean is that with a decrease in the value of x, the value of f(x) moves closer to 0
Hence, as the domain value moves closer to negative infinity, the value of the range moves closer to 0. Furthermore, as the value of the domain moves closer to positive infinity, the value of the range also close in on positive infinity
The above situation is for a being positive (given as 2)
Now, when a becomes negative, we have an opposite direction for the plot
Although, as the domain value moves closer to negative infinity, we have the value of f(x) being closer to zero. This is directly as above
However, as the domain moves towards positive infinity, the value of the range moves closer to negative infinity
In summary;
[tex]\begin{gathered} \text{for a = 2} \\ x\Rightarrow\text{ +}\infty\text{ , f(x)}\Rightarrow+\infty \\ x\Rightarrow-\infty,\text{ f(x) }\Rightarrow0 \\ \text{for a = -2} \\ x\Rightarrow+\infty,\text{ f(x)}\Rightarrow-\infty \\ x\Rightarrow-\infty,\text{ f(x)}\Rightarrow0 \end{gathered}[/tex]Josslyn placed $4400 in a savings account which earns 3.2% interest, compounded continuously. How much will she have in the account after 8 years? Round your answer to the nearest dollar. Do NOT round until you have calculated the final answer.
Answers
The initial amoud on her savings is $4400, so now we can calculate the interest that she generate in one year:
[tex]4400\cdot\frac{3.2}{100}=140.8[/tex]so in 8 year is going to be:
[tex]140.8\cdot8=1126.4[/tex]So the total amoud will be the initial amound plus the interest she earn so:
[tex]4400+1126.4=5526.4[/tex]and rounded would be like:
[tex]5526\text{ dollars}[/tex]Answer:5684
Step-by-step explanation:
pe
I want to select average students . If the mean score on the qualifying test is 43.2 and the standard deviation is 8.6. find the score that cutt off the middle 50 percent of all scores
Answers
The score that cutt off the middle 50 percent of all scores is 43.2
Explanations:For a normal distribution, the normal value is the mean
It divides the curve in 50%-50%
Mean score, μ = 43.2
Standard Deviation, σ = 8.6
P(X≤a)=0.5
Use Z =(X-μ)/δ ~N(0;1)
b =(a-μ)/σ
P(Z≤b)=0.5
The value is b=0 (the mean for Z)
a=(b*σ)+μ
a=(0*8.6)+43.2
a=43.2
Therefore, the score that cutt off the middle 50 percent of all scores is 43.2
Number of Hours13.5Total Cost$2.00$6.50$7.00$9.00$12.507.59Identify the domain and range. Select the two correct answers.АDomain: {1, 2.00}BDomain: (1.3.5, 5, 7.5,9)CDomain: 2. 6.50, 7.9. 12.50)DRange: 19. 12.50)ERange: (1,3,5,5, 7.5.9}F.Range: (2,6 50, 7, 9, 12.50)
Answers
Domain is the set of x values, or the inputs.
Range is the set of y values, or the outputs.
They are unique.
Looking at the table,
the number of hours is the input on which we have the cost, the output.
So,
We get domain from number of hours
We get range from total cost
1, 3.5, 5, 7.5, and 9 ---- hours (domain)
B is right.
Now,
Range would be the total costs, which are:
2, 6.5, 7, 9, 12.5
F is right.
Correct answers are B and F
Assume that the random variable X is normally distributed , with mean = 80 and standard deviation = 15. Compute the probability P(X > 92) .
Answers
Assume that the random variable X is normally distributed , with mean = 80 and standard deviation = 15. Compute the probability P(X > 92) .
step 1
Find z score
z=(92-80)/15
z=0.8
step 2
using the z-score table
For z=0.8
P=0.7881
therefore
answer is
P=0.7881Part 1 - FlooringFor the most part, the floors in Rachel's new house are in good shape. However, there are a couple of rooms that Rachel wants to redo right away. She plans to put new carpet in the family room and living room, and fresh hardwood floors in the foyer and kitchen. She also needs to put a new tile floor in the breakfast nook and mud room. Rachel (with your help) plans to install all the flooring herself, so there are no labor costs. However, she does need to buy the materials.Rachel has already scoped out the local home improvement store and priced out the cost of each material. She found that the carpet she wants will cost $1.80 per square foot, the hardwood flooring will cost $4.50 per square foot, and the tiles will cost $2.30 per square foot.a. How many square feet of carpet does Rachel need?b. How many square feet of hardwood does Rachel need?c. How many square feet of tile does Rachel need?d. How much will the total cost of materials for the re-flooring project be?
Answers
ANSWERS
a. 863.08 ft²
b. 474 ft²
c. 249 ft²
d. $4,259.24
EXPLANATION
Given:
• Rooms with ,carpet,: Family room and living room
,• Rooms with ,hardwood,: kitchen and foyer
,• Rooms with ,tiles,: breakfast nook and mudroom
• Cost ,carpet,: $1.80 per square foot
,• Cost ,hardwood,: $4.50 per square foot
,• Cost ,tiles,: $2.30 per square foot
First, we have to find the area of each of the mentioned rooms,
a. The family room is in the shape of a square whose sides are all 20 feet and a semicircle whose diameter is 20 feet. The area of the family room is the sum of the areas of each of these figures,
[tex]A_{family-room}=(20ft\cdot20ft)+(\frac{1}{2}\cdot\pi\cdot(20ft/2)^2)[/tex]As shown above, the area of the semicircle is half the area of the full circle with the same diameter. Solve,
[tex]A_{family-room}\approx(400ft^2)+(157.08ft^2)=557.08ft^2[/tex]The living room is in the shape of a rectangle with side lengths 15ft and 22ft, but a right triangle is cut out from the corner. The area of the living room is the area of the mentioned rectangle minus the area of the triangle of the corner,
The side lengths of the triangle are 15ft - 9ft = 6ft and 22ft - 14ft = 8ft. The area of the triangle is,
[tex]A_{triangle}=\frac{6ft\cdot8ft}{2}=24ft^2[/tex]So, the area of the living room is,
[tex]A_{living-room}=(22ft\cdot15ft)-24ft^2=330ft^2-24ft^2=306ft^2[/tex]The area that Rachel wants to cover with a new carpet is,
[tex]A_{carpet}=A_{family-room}+A_{living-room}=557.08ft^2+306ft^2=863.08ft^2[/tex]Hence, the area to be covered with carpet is 863.08 ft².
b. The kitchen is a rectangle with dimensions 24 ft and 15 ft, so its area is,
[tex]A_{kitchen}=24ft\cdot15ft=360ft^2[/tex]The foyer is in the shape of a rectangle with dimensions 10ft and 15ft. However, assuming that the stairs won't be covered with hardwood and that they cover that part of the foyer's floor, to find the area we have to subtract the area the stairs occupy in that room.
The rectangle where the stairs are has dimensions 9ft and (10ft - 6ft ) = 4ft. The area of the Foyer is,
[tex]A_{foyer}=(10ft\cdot15ft)-(9ft\cdot4ft)=(150ft^2)-(36ft^2)=114ft^2[/tex]The area Rachel wants to be covered by hardwood is the sum of the two,
[tex]A_{hardwood}=A_{kitchen}+A_{foyer}=360ft^2+114ft^2=474ft^2[/tex]Hence, the area to be covered with hardwood is 474 ft².
c. The mudroom is in the shape of a rectangle with dimensions 15 ft and 7 ft, so its area is,
[tex]A_{mudroom}=15ft\cdot7ft=105ft^2[/tex]The breakfast nook is in the shape of a trapezoid, where the height is 8ft and the lengths of the bases are 24ft and 12ft. Its area is,
[tex]A_{breakfast-nook}=\frac{(12ft+24ft)}{2}\cdot8ft=\frac{36ft}{2}\cdot8ft=18ft\cdot8ft=144ft^2[/tex]The area Rachel wants to cover with tiles is the sum of these two areas,
[tex]A_{tiles}=A_{mudroom}+A_{breakfast-nook}=105ft^2+144ft^2=249ft^2[/tex]Hence, the area to be covered with tiles is 249 ft².
d. Finally, we have to find the cost of flooring with each material,
[tex]Costs=\begin{cases}C_{carpet}=A_{carpet}\cdot p_{carpet}=863.08ft^2\cdot1.80=1,553.54 \\ C_{hardwood}=A_{hardwood}\cdot p_{hardwood}=474ft^2\cdot4.50=2,133 \\ C_{tiles}=A_{tiles}\cdot p_{tiles}=249ft^2\cdot2.30=572.70\end{cases}[/tex]The total cost of the project is the sum of the three,
[tex]C_{project}=C_{carpet}+C_{hardwood}+C_{tiles}=1,553.54+2,133+572.70=4,259.24[/tex]Hence, the total cost of the re-flooring project will be $4,259.24.
Given the functions:Evaluate the function for . Write your answer in exact simplified form. Select "Undefined" if applicable.
Answers
Given:
[tex]\begin{gathered} f(x)\text{ = x}^3\text{ + 6x} \\ g(x)\text{ = }\sqrt{2x} \end{gathered}[/tex]Explanation:
The required function is given as,
[tex]undefined[/tex]Describe how you can use the factors of a quadratic function to find its zeroes. (Please try to answer it specifically)
Answers
Oce we have the factors, we must equal each factor to zero, then we solve for x to find the zeroes of the equation.
Ex.
(x - 3)(x + 2) = 0
the factors are (x - 3) and (x + 2)
Equal to zero
x - 3 = 0 x + 2 = 0
Solve for x
x = 3 x = -2 and these are the zeroes of the
equation.
Answer:
To find de ceros you can take each factor and use the 0 product property, then you solve to find the value of the cero.
A card is chosen at random from a deck of 28 cards. The deck contains red, 12 black 7 blue, and 2 green cards. Thend the card is returned to the deck and New card is cosen. the table below shows the results of choosing 14 cards. for which color of card is the experimental probability the same as the theoretical probabicaras.Results red= 10 black=2 blue=1green=1
Answers
From the question, we can find that we have 7 red cards
so, the probability of chosen at random a card is
p(red)= 7/28
p(black)= 12/28
p(blue) = 7/28
p(green)=2/28
As after picking a card we return the card to the deck, and given that we chose 14 cards, our theoretical number of chosen cards should be around
p(red) = (7/28)x14 = 3.5
p(black) = (12/28)x14 = 6
p(blue) = (7/28)x14 = 3.5
p(green)= (2/28)x14=1
so the color that the experimental probability is the same as the theoretical probability is green
How much interest is earned on an initial investment of $700 with a 5% annual rate for 2 years? A $700B $350C $70D $35
Answers
Let's calculate the 5% of $700 using a rule of three:
This way,
[tex]\begin{gathered} x=\frac{700\cdot5}{100} \\ \Rightarrow x=35 \end{gathered}[/tex]$35 is earned each year, For two years, the earnings would be $70
Answer: C. $70
Match the equation in Column I with the correct description in Column II
Answers
As given by the question
There are given that the equations:
Now,
According to the given question,
The correct matching values are;
[tex]\begin{gathered} (a)\rightarrow E \\ (b)\rightarrow D \\ (c)\rightarrow C \\ (d)\rightarrow B \\ (e)\rightarrow A \end{gathered}[/tex]Solve this problem, please and thank you. Picture included. Algebra 2.
Answers
List the sides of ABC from shortest to longest.CB AB ACАВ, СВ, АСАВ, АС, СВCB AC AB
Answers
First we need to calculated the missing angle
the intern angles of a triangle must be 180°
angle +63+60=180
angle=57
the shortest side is AB
the next side is AC
and the longest side is CB
t
Persuade Mr. Zion whether the numbers 12,16,and 20 make a right triangle or not. Make sure to state reasons for and against your belief
Answers
we can corrobarate this using pythagorean theorem:
[tex]\begin{gathered} c^2=a^2+b^2 \\ \text{where:} \\ c>a,c>b \end{gathered}[/tex]Let:
[tex]\begin{gathered} a=12 \\ b=16 \\ c=20 \\ 20^2=12^2+16^2? \\ 400=144+256 \\ 400=400 \\ \end{gathered}[/tex]since the equality is satisfied, we can conclude that it is possible to make a right triangle using those numbers
Please answer and explain the problem. This is due soon, please help!!
Answers
In all cases use the following formula for the are of a rectangular shape:
A = lw
Plot A:
The area and height are known, then, solve the formula for the length l:
l = A/w
repace the given values
l = (204 ft²)/(10.2 ft)
I = 20 ft
For the perimeter you have:
P = 2l + 2w = 2(20 ft) + 2(10.2 ft) = 60.4ft
Plot B:
The length and the perimeter are known. For the expression for the perimeter solve for w:
P = 2l + 2w
w = (P - 2l)/2
replace the values of P and l:
w = (57.56 ft - 2(12.78 ft))/2 = 16 ft
Then, replace in the formula for the area:
A = lw = (12.78 ft)(16 ft) = 204.48 ft²
Plot C:
The area and the height are known. Use the formula for A to obtain the length:
l = A/w = 204.49 ft/14.3 ft = 14.3 ft
and for the perimeter:
P = 2w + 2l = 2(14.3 ft) + 2(14.3 ft) = 57.2 ft
Hence, you can conclude:
- The plost with the least amount of fencing is the plot with the lowest perimeter, hence, Plot C requires the least amount of fencing.
- The plot with the greatest area is Plot A.
solve for C -3 (C + 5)- (c-3)=32
Answers
Given the equation:
[tex]-3(c+5)-(c-3)=32[/tex]To find the value of 'c', the first step to do is to get rid of the parenthesis. We can do this using the distributive property on both cases:
[tex]\begin{gathered} -3(c+5)-(c-3)=32 \\ \Rightarrow-3\cdot c+(-3)\cdot5-c-(-3)=32 \\ \Rightarrow-3c-15-c+3=32 \end{gathered}[/tex]Now that we don't have any parenthesis in our equation, we start moving similar terms: we leave on the left the terms with the variable 'c' and we move the rest of the terms to the right side with it's sign changed:
[tex]\begin{gathered} -3c-15-c+3=32 \\ \Rightarrow-3c-c=32+15-3 \end{gathered}[/tex]We can make the operations on each side since now we have the similar terms apart:
[tex]\begin{gathered} -3c-c=32+15-3 \\ \Rightarrow-4c=47-3=44 \\ -4c=44 \end{gathered}[/tex]Finally, we move the -4 that is multiplying the 'c' to the other side doing its opposite operation:
[tex]\begin{gathered} -4c=44 \\ \Rightarrow c=\frac{44}{-4}=-11 \\ c=-11 \end{gathered}[/tex]therefore, c=-11