consider the following.find formula simplify answer .Find the domain for the formula and round answer to two decimal places if necessary.
Answers
The sum of functions is given as:
[tex](f+g)(x)=f(x)+g(x)[/tex]In this case we have:
[tex](f+g)(x)=5x+\sqrt[]{x-1}[/tex]The domain of the functions is any number that makes the squared root a real number, then:
[tex]\begin{gathered} x-1\ge0 \\ x\ge1 \end{gathered}[/tex]Hence the domain of the functions is:
[tex]\lbrack1,\infty)[/tex]Related Questions
I just really need help I don’t know that much about math I was in special Ed math and got kicked out I just need help and need to be shown what I’m doing
Answers
Given:
15 pounds of barrel
10 gallons of water; 98.4 pounds
20 gallons of water; 181.8 pounds
In order to find the equation and graph that matches this, we need to find the following:
y - intercept
slope of the line
In the problem, it was given that the barrel weighs 15 pounds. Meaning, even in an empty barrel, we already have a total weight of 15 pounds.
We let:
x = gallons of water
y = total weight
This means, at x = 0, y = 15.
y - i
1/2 n + 3 < 5 how would it be shown on a graph
Answers
To solve this inequality we need to isolate the variable "n" on the left side.
[tex]\frac{1}{2}n<5-3[/tex]Since there was a "+3" on the left side we needed to change its side, by inverting the number's signal.
[tex]\begin{gathered} \frac{1}{2}n<2 \\ n<2\cdot2 \\ n<4 \end{gathered}[/tex]Since the variable we need to calculate was multiplying "1/2" we needed to multiply both sides by 2 in order to find its value. The solution is n < 4.
Find the shaded area (round answer to 3 sig figs).
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1. Let us find the area of the sector:
[tex]\begin{gathered} \frac{\theta}{360}\cdot\pi\cdot r^2\text{ (Area of a sector formula)} \\ \frac{85}{360}\cdot\pi\cdot(12\operatorname{cm})^2\text{ (Replacing)} \\ \frac{85}{360}\cdot\pi\cdot144cm^2\text{ (Raising 12 to the power of 2)} \\ 0.236\cdot\pi\cdot144cm^2\text{ (Dividing)} \\ 106.814cm^2\text{ (Multiplying)} \end{gathered}[/tex]2. The area of the triangle would be:
[tex]\begin{gathered} At=\frac{1}{2}\cdot ab\cdot\sin (\theta)\text{ (Area of a non right-angled triangle)} \\ At=\frac{1}{2}\cdot(12)\cdot(12)\cdot\sin (85)\text{ (Replacing)} \\ At=71.726cm^2 \end{gathered}[/tex]3. Subtracting the area of the triangle from the area of the sector, we have:
106.814 cm^2 - 71.726 cm^2 = 35.088 cm^2
The answer is 35.088 cm^2
If segments WY and XZ are diameters of circle T, and WY=XZ=6. If minor arc XY= 140 degrees, what is the length of arc YZ?
Answers
hello
to solve this question, we need to draw an illustration
since we are looking for the major arc, we would subtract the minor arc from 360 degrees
major arc YZ =
[tex]\begin{gathered} yz=360-xy \\ yz=360-140=220 \end{gathered}[/tex]now, we know the angke on the major arc is equal to 220 degrees, we can use this information to solve for the length of the arc.
length of an arc
[tex]\begin{gathered} L_{\text{arc}}=\frac{\theta}{360}\times2\pi r \\ \theta=angle \\ r=\text{radius} \\ \pi=3.14 \end{gathered}[/tex]but in this question, we were given the diameter of two segements. we can use that information to solve for the radius
[tex]\begin{gathered} radius=\frac{diameter}{2} \\ \text{diameter}=wx=xz=6 \\ \text{radius(r)}=\frac{6}{2}=3 \end{gathered}[/tex]let's insert this and other variables into our equation
[tex]\begin{gathered} L_{\text{arc}}=\frac{\theta}{360}\times2\pi r \\ \text{L}_{\text{arc}}=\frac{220}{360}\times2\times3.14\times3 \\ L_{\text{arc}}=11.513 \end{gathered}[/tex]from the calculations above, the length of the arc YZ is equal to 11.513
A group of friends will buy at most 8 snacks at a movie theater and spend no more than $42. They will pay $4.00 for each box of candy and $7.00 for each bag of popcorn. The system of inequalities graphed below represents this information.
Answers
Let x = candy , y = popcorn
so,
the cost of one box of candy = $4
The cost of one bag of popcorn = $7
so, the solution of part A
The system of inequalities represents the situation is as following:
[tex]\begin{gathered} x+y\leq8 \\ 4x+7y\leq42 \end{gathered}[/tex]========================================================================
Part B:
We need to find which combination of candy and popcorn could the group buy:
a. 2 candy and 6 popcorn
check for the first inequality : 2 + 6 = 8
check for the second inequality : 2 * 4 + 7 * 6 = 8 + 42 = 50 > 42
So, this option is wrong
b. 3 candy and 4 popcorn
check for the first inequality : 3 + 4 = 7 < 8
check for the second inequality : 4 * 3 + 7 * 4 = 12 + 28 = 40 < 42
So, this option is true
c. 5 candy and 4 popcorn
check for the first inequality : 5 + 4 = 9 > 8
So, this option is wrong
d. 8 candy and 1 popcorn
check for the first inequality : 8 + 1 = 9 > 8
So, this option is wrong
so, the answer of part B is:
option b
the group could by 3 boxes of candy and 4 bags of popcorn
solve the equation Mentally
Answers
Given:-
[tex]\begin{gathered} 8+j=15 \\ \end{gathered}[/tex]To Find:-
The value of j.
To find the value of j, we need to keep j at one side of the equal to sign and take all other number to the other side of the equal to sign.
[tex]\begin{gathered} 8+j=15 \\ j=15-8 \\ j=7 \end{gathered}[/tex]So now the value of j has been found. The value of j is 7.
What is the approximate Probability of drawing a spade Card from a standard deck of shuffled cards?Group of answer choices1/21/41/5212/52
Answers
Given,
The number of cards in a standard deck is 52.
Required:
The probability of drawing of spade card.
The number of spade card in deck is 13.
Consider,
A is the event of drawing of spade card.
Probability is calculated as:
[tex]Probability\text{ =}\frac{Number\text{ of favourable events}}{Total\text{ events}}[/tex]Substituting the values then,
[tex]\begin{gathered} P(A)\text{=}\frac{N(A)}{Total\text{ events}} \\ =\frac{13}{52} \\ =\frac{1}{4} \end{gathered}[/tex]Hence, the probability is 1/4.
Exhibit 6-4The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000.Refer to Exhibit 6-4. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000?
Answers
Given:
Normally distributed = $40,000
a standard deviation= $5,000.
Required:
Find the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000.
Explanation:
The probability formula when the mean and standard deviation is known:
[tex]P(x)=P(\frac{x-mean}{standard\text{ deviation}})[/tex][tex]\begin{gathered} P(x\ge30k)=P(\frac{30k-40k}{5k}) \\ \begin{equation*} P(x\ge30k)= \end{equation*} \end{gathered}[/tex]
How do you subtract 5/6 - 5/9 then write it as a fraction in simplest form?
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To subtract two fractions we can use the following:
[tex]\frac{a}{b}-\frac{c}{d}=\frac{(a\cdot d)-(b\cdot c)}{b\cdot d}[/tex]So 5/6 - 5/9 is equal to:
[tex]\frac{5}{6}-\frac{5}{9}=\frac{(5\cdot9)-(6\cdot5)}{6\cdot9}=\frac{45-30}{54}=\frac{15}{54}[/tex]Finally, we can simplify the fraction dividing the numerator and denominator by 3, as:
[tex]\frac{15}{54}=\frac{15/3}{54/3}=\frac{5}{18}[/tex]So, the answer is 5/18
Answer: 5/18
Estimate 20 x 37 x 21/5 ÷ 98. Is it an overestimate or underestimate? Explain.
Answers
20 x 37 x 21/5 ÷98
Find if 20 x 37 x 21/5 is bigger or lower than 98
20x37x21/5= 15540/5= 3108
Then 3108/98 is an overestimate
= 3108/98=31. 71
Answer is 31.71
С.c7. The difference of two positive numbers is six. Their product is 223 less than the sum of their squares. Whatethe two numbers?
Answers
Let two unknow positive number is "x" and "y"
Difference of two positive number is 6 that mean:
[tex]x-y=6[/tex]Their product is 223 less than the sum of their square:
[tex]\begin{gathered} x\times y=x^2+y^2-223 \\ xy=x^2+y^2-223 \end{gathered}[/tex]Substitute x with variable y:
So,
[tex]\begin{gathered} x-y=6 \\ x=6+y \end{gathered}[/tex]Put the value of "x" in another equation:
[tex]\begin{gathered} xy=x^2+y^2-223 \\ (6+y)y=(6+y)^2+y^2-223 \\ 6y+y^2=36+y^2+12y+y^2-223 \\ y^2+6y-187=0 \\ y^2+17y-11y-187=0 \\ y(y+17)-11(y+17)=0 \\ (y+17)(y-11)=0 \\ y=-17;y=11 \end{gathered}[/tex]Given number is positive that mean y=11 and so value of x is:
[tex]\begin{gathered} x=6+y \\ x=6+11 \\ x=17 \end{gathered}[/tex]So the number is 11 and 17.
2) write the equation of a line that passes through the point ( 4, 5) and is perpendicular to a line that passes through the points ( 6 8) and (10 0)
Answers
We have the following:
First we calculate the slope of the line where we are given two points (6,8) and (10,0)
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]repplacing:
[tex]m=\frac{0-8}{10-6}=\frac{-8}{4}=-2[/tex]now, when two lines are perpendicular:
[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ -2=-\frac{1}{m_2} \\ 2=\frac{1}{m_2} \\ m_2=\frac{1}{2} \end{gathered}[/tex]now,
[tex]y=mx+b[/tex]with the point (4,5), replacing:
[tex]\begin{gathered} 5=\frac{1}{2}\cdot4+b \\ 5=2+b \\ b=5-2 \\ b=3 \end{gathered}[/tex]Therefore, the equation is:
[tex]\begin{gathered} y=\frac{1}{2}x+3 \\ y=\frac{x}{2}+3 \end{gathered}[/tex]check:
[tex]\begin{gathered} y=\frac{4}{2}+3 \\ y=2+3 \\ y=5 \end{gathered}[/tex]Therefore, the answer is y = x/2 + 3
find the first two common multioles of 3, 4, and 6
Answers
The first common multiple of 3, 4 and 6 is 12
The second common multiple of 3, 4 and 6 is 24
give an example of a positive tempature and a negative tempature that have a diffrence of 5 fedagree
Answers
We can think of temperatures above zero F and below zero F. For example weather conditions in cold places like Alaska.
In the morning, the temperature could be 2 degrees F (above zero)), but later towards the night, the temperature could be below zero in three units : -3 degrees F.
So the difference is the distance from zero to 2 (above) and the distance to zero from below 3 (below the zero mark. so these two differences from zero add up as 2 + 3 = 5
The way to do such in one go with math is to write the "difference" (normally associated with a SUBTRACTION, of the form: 2 - (-3), and therefore use that the negative (or opposite) of a negative number is a positive number:
- (-3) = +3
The same happens when we want to compare the difference between
9 - (-15) = 9 + 15 = 24
with the difference:
-15 - 9 = -24
The important thing is to consider the absolute value if we just want to find the number of units between the values, how many units they are separated.
And if we need to find what needs to be added or subtracted to one of them, at that point the sign of the difference is critical. This is because in one case we will need to add to get to the other number, while in the other case we need to subtract.
Consider the following functions. Find four ordered pairs that satisfy the function
Answers
Since the function f(x) is
[tex]f(x)=\sqrt[]{x-7}[/tex]Since there is no square root for negative numbers, then
[tex]x-7\ge0[/tex]We will solve it by adding 7 to both sides
[tex]\begin{gathered} x-7+7\ge0+7 \\ x\ge7 \end{gathered}[/tex]Then we can choose values of x from 7 and greater
Let x = 7
[tex]\begin{gathered} f(7)=\sqrt[]{7-7} \\ f(7)=\sqrt[]{0} \\ f(7)=0 \end{gathered}[/tex]The 1st ordered pair is (7, 0)
Let x = 11
[tex]\begin{gathered} f(11)=\sqrt[]{11-7} \\ f(11)=\sqrt[]{4} \\ f(11)=2 \end{gathered}[/tex]The 2nd ordered pair is (11, 2)
Let x = 8
[tex]\begin{gathered} f(8)=\sqrt[]{8-7} \\ f(8)=\sqrt[]{1} \\ f(8)=1 \end{gathered}[/tex]The 3rd ordered pair is (8, 1)
Let x = 16
[tex]\begin{gathered} f(16)=\sqrt[]{16-7} \\ f(16)=\sqrt[]{9} \\ f(16)=3 \end{gathered}[/tex]The 4th ordered pair is (16, 3)
The 4 ordered pairs are (7, 0), (8, 1), (11, 2), (16, 3)
What is the value of x in the triangle below?2460O 12813O 122O 12/3
Answers
The question gives us a right-angled triangle and find the value of x.
In order to solve the problem, we use SOHCAHTOA. In this case, we will use "SOH" from SOHCAHTOA because we have the Opposite as x and Hypotenuse as 24, while the relevant angle is 60 degrees.
Let us apply this formula:
[tex]\begin{gathered} \text{ SOH implies:} \\ \sin \theta=\frac{\text{Opposite}}{\text{Hypotenuse}} \\ \\ \theta=60^0,\text{Opposite}=x,\text{Hypotenuse}=24 \\ \\ \therefore\sin 60^0=\frac{x}{24} \end{gathered}[/tex]We simply need to make x the subject of the formula and we shall also represent sin 60 with its surd form.
This is done below:
[tex]\begin{gathered} \sin 60^0=\frac{x}{24} \\ \text{ Multiply both sides by 24} \\ 24\times\sin 60^0=\frac{x}{24}\times24 \\ \therefore x=24\times\sin 60^0 \\ \\ \sin 60^0=\frac{\sqrt[]{3}}{2} \\ \\ x=24\times\frac{\sqrt[]{3}}{2}=12\times2\times\frac{\sqrt[]{3}}{2}\text{ (2 crosses out)} \\ \\ x=12\sqrt[]{3} \end{gathered}[/tex]Therefore, the final answer is Option 4
2. Tricky Flips sells a coin that promises to land on heads 3 out of every 4 times. If the coin isflipped 20 times, which of the following is the number of times you should expect it to landon head
Answers
Given:
Number of times head shows up out of 4 trials = 3
Number of trials = 20
Solution
The number of times (N) head shows up for each trial:
[tex]\begin{gathered} N\text{ = }\frac{Number\text{ of times head shows up out of 4 trials}}{Number\text{ of trials}} \\ =\text{ }\frac{3}{4} \end{gathered}[/tex]The number of times we would expect head to show up for 20 trials:
[tex]\begin{gathered} =\text{ }\frac{3}{4}\text{ }\times\text{ 20} \\ =\text{ 15 times} \end{gathered}[/tex]Answer: 15 times
John is listing each step of the equation +4 = 10 – 3 폼 5+4= 10 - 3 *5 = +4= 7 c+4= -35 TE -39 What was his mistake?
Answers
Answer:
x+ 4= -35
Explanation:
Given the equation:
[tex]\frac{x}{-5}+4=10-3[/tex]The next step is:
[tex]\frac{x}{-5}+4=7[/tex]The next step should have been:
[tex]\begin{gathered} \frac{x}{-5}=7-4 \\ \frac{x}{-5}=3 \end{gathered}[/tex]Therefore, his mistake was the step below:
[tex]x+4=-35[/tex]A farmer fell asleep under a tree in his apple orchard while thinking about pie. While he was sleeping, a squirrel knocked an apple off a branch of the tree. The function f (d) = (see photo) can be used to find the amount of time in seconds that it takes for the apple to drop acertain distance d, where d is in meters.Step 1 of 3 : If the apple was connected to a branch that was 3 meters above the farmer's head, how long would it take before the applehit the top of the farmer's head? Round your answers to the nearest hundredth.
Answers
Solution
Step 1
Write the time function equation
[tex]f(d)\text{ = }\sqrt{\frac{2d}{9.8}}[/tex]Step 2
d = 3 meters
[tex]\begin{gathered} f(3)\text{ = }\sqrt{\frac{2\times3}{9.8}} \\ f(3)\text{ = 0.78 seconds} \end{gathered}[/tex]Final answer
0.78 seconds
1) Is F increasing on the interval (2.10)? 2) List the interval(s) on which F is increasing. Justify your answer. 3) List the intervalis) on which F is decreasing Justify your answer. 4)List the value(s) of x at which has a local maximum. Justify your answer.5) List the value(s) of x at which F has a local minimum. Justify your answer. 6) Find the X -intercepts 7) Find the Y-intercepts.
Answers
1)
in the interval (2,5) decreases and then increases , but We cant say that it is growing since it had a fall in the middle, so isnt increasing
2)
(-8,-2) (0,2) (5,10)
It is increasing because, from left to right, it comes from a low point to a higher point
3)
(-10,-8) (-2,0) (2,5)
It is decreasing because, from left to right, it comes from a high point to a lower point
4)
x=-2 and 2
are the highest values of the function
5)
x=-8, 0 and 5
are the lowest values of the function
6)
x=-5, 0 and 5
values where y = 0, therefore intersects the x axis
7)
y=0
values where x = 0, therefore intersects the y axis
Find the range of the graphed function.A. -9 < y < 5B. y is all real numbers.C. O < y < 10D. y > 0
Answers
The range of a function is all the values that the function can take on the y-axis.
So, the y values of this function are between -9 and 5.
It means that the range is:
A. -9 < y < 5
Which of the following graphs shows a positive linear relationship with acorrelation coefficient, r, close to 1?A.B.D.A. Graph AОСB. Graph BO C. Graph CO D. Graph DPREVIOUSreAOO
Answers
Given:
The objective is to choose the correct graph which shows a positive linear relationship with a correlation coefficient, r, close to 1.
The positive linear relationship represents the increasing values of plots from origin to positive x and positive y axis.
By observing graph A, the plots are scattered all over the quadrant. Hence, it is a weak association.
By observing graph B, the plots are plotted as decreasing in y axis and increasing in x axis. Hence, it is a strong negative association.
By observing graph C, the plots are plotted as increasing in both x axis and y axis. Hence, it is a strong positive association.
Hence, the graph which shows a positive linear relationship with a correlation coefficient, r, close to 1 is graph C.
1) cos X Z 41 40 X 9Y 41 40 A) B) 9 41 9 C) 40 D) 41
Answers
Given data:
The given right angle triangle.
The expression for cos(X) is,
[tex]\begin{gathered} \cos (X)=\frac{XY}{XZ} \\ =\frac{9}{41} \end{gathered}[/tex]Thus, the value of cos(X) is 9/41, so the correct option is (C).
Write the equation of the line that is perpendicular to the line 8y−16=5x through the point (5,-5).A. y=5/8x+3B. y=−8/5x−3C. y=−8/5x+3D. y=8/5x+3
Answers
Given the equation of the line below,
[tex]8y-16=5x[/tex]If the line passes through the point,
[tex](5,-5)[/tex]Re-writing the eqaution of the line in slope intercept form,
[tex]\begin{gathered} 8y-16=5x \\ 8y=5x+16 \\ \text{Divide both sides by 8} \\ y=\frac{5x}{8}+\frac{16}{2} \\ y=\frac{5}{8}x+2 \end{gathered}[/tex]The slope of the perpendicular line is the negative reciprocal of the slope of the eqaution of the line in the slope-intercept form given above
The general form of the slope-intercept form of the equation of a straight line is,
[tex]\begin{gathered} y=mx+c \\ \text{Where m is the slope} \\ y=\frac{5}{8}x+2 \\ m=\frac{5}{8} \\ \text{Slope of the perpendicular line is} \\ m_1=-\frac{1}{m} \\ m_{1_{}}=-\frac{1}{\frac{5}{8}}=-1\times\frac{8}{5}=-\frac{8}{5} \end{gathered}[/tex]The formula to find the equation of a line with point (5, -5) below is,
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=m_1 \\ \text{Where} \\ (x_1,y_1)=(5,-5) \\ m_1=-\frac{8}{5} \end{gathered}[/tex]Substitute the values into the formula of the eqaution of a straight line,
[tex]\begin{gathered} \frac{y-(-5)}{x-5}=-\frac{8}{5} \\ \frac{y+5}{x-5}=-\frac{8}{5} \\ \text{Crossmultiply} \\ 5(y+5)=-8(x-5) \\ 5y+25=-8x+40 \\ \text{Collect like terms} \\ 5y=-8x+40-25 \\ 5y=-8x+15 \\ \text{Divide both sides by 5} \\ \frac{5y}{5}=-\frac{8}{5}x+\frac{15}{5} \\ y=-\frac{8}{5}x+3 \end{gathered}[/tex]Hence, the right option is C
Order these numbers from least to greatest.0,1,1/2,10/11,51/100,24/50 and 3/20
Answers
From least to greatest, the numbers are:
0, 3/20, 24/50, 1/2, 51/100, 10/11 and 1
Explanation:Given the numbers:
0, 1, 1/2, 10/11, 51/100, 24/50 and 3/20
From least to greatest, they are:
0, 3/20, 24/50, 1/2, 51/100, 10/11 and 1
Graph the line with slope -3/4 passing through the point (4,3)
Answers
The graph is displayed after the explanation
Explanation:The slope is rise/run = -3/4
The line passes through (4, 3)
The run is 4, we add 4 to the x-coordinate
The rise is -3, we add -3 to the y-coordinate
We have:
(4 + 4, 3 - 3) = (8, 0)
We use (4, 3) and (8, 0) to graph the line
The graph is shown below:
how would I figure this out (this assignment is just a practice but I dont have any notes to look off of and I'm confused)
Answers
We have the following:
We have the following points that are on the graph:
(-2, 1); (0, -1); (2, 1); (4, 3)
We must evaluate each point in the functions to know which is correct
F
y = x - 1
[tex]y=-2-1=-3[/tex]the first point does not match, therefore this function is not correct
H
y = x^2 - 1
[tex]y=(-2)^2-1=4-1=3[/tex]the first point does not match, therefore this function is not correct
G
y = |x| - 1
[tex]\begin{gathered} y=|-2|-1=2-1=1 \\ y=|0|-1=0-1=-1 \\ y=|2|-1=2-1=1 \\ y=|4|-1=4-1=3 \end{gathered}[/tex]In this function, all the points coincide, therefore the answer to the question is the function G
Hello,Can you help me with the question in the photo?Thank you,
Answers
Answer:
4, 12, 44, and 173.
Explanation:
Given the recursion formula:
[tex]\begin{gathered} a_n=4a_{n-1}-4 \\ a_1=4,n\geqslant2 \end{gathered}[/tex]We want to find the first four terms of the sequence.
[tex]\begin{gathered} a_2=4a_{2-1}-4=4a_1-4=4(4)-4=16-4=12 \\ \implies a_2=12 \end{gathered}[/tex]Similarly:
[tex]\begin{gathered} a_3=4a_{3-1}-4=4a_2-4=4(12)-4=48-4=44 \\ \implies a_3=44 \end{gathered}[/tex]Finally:
[tex]\begin{gathered} a_4=4a_{4-1}-4=4a_3-4=4(44)-4=176-4=173 \\ \implies a_4=173 \end{gathered}[/tex]The first four terms of the sequence are 4, 12, 44, and 173.
f(x)=x^2+2x+4Evaluate f(x+5).Simplify the answer
Answers
We have a function:
[tex]f(x)=x^2+2x+4[/tex]We have to evaluate f(x+5).
To do so, we replace the argument x from the definition of f(x) with "x+5":
[tex]f(x+5)=(x+5)^2+2(x+5)+4[/tex]Now, we can expand this and simplify as:
[tex]\begin{gathered} f(x+5)=(x+5)^2+2(x+5)+4 \\ f(x+5)=(x^2+2\cdot5x+5^2)+(2x+10)+4 \\ f(x+5)=x^2+10x+25+2x+10+4 \\ f(x+5)=x^2+12x+39 \end{gathered}[/tex]Answer: f(x+5) = x² + 12x +39
Practice Skills_Simplifying Equations1. 3( 1/2 - y) = 3/5 + 15y. What isthe solution to the given equation?
Answers
You have the following equation:
3(1/2 - y) = 3/5 + 15y
In order to solve the previous equation you proceed as follow:
3(1/2 - y) = 3/5 + 15y eliminate parenthesis
3/2 - 3y = 3/5 + 15y multiply by 5 both sides
15/2 - 15y = 3 + 75y multiply by 2 both sides
15 - 30y = 6 + 150y sum 30y both sides and subtract 6 both sides
15 - 30y + 30y - 6 = 6 + 150y + 30y - 6 simplify
9 = 180y divide by 180 both sides
9/180 = 180y/180 simplify
1/20 = y
(the multiplication by 5 and 2 is for eliminating denominator with the same number)
Hence, the solution to the given equation is y = 1/20