By definition, a fraction has the following form:
[tex]\frac{a}{b}[/tex]When "a" is the numerator and "b" is the denominator.
In this case you have the following fractions:
[tex]\begin{gathered} \frac{2}{5} \\ \\ \frac{3}{10} \end{gathered}[/tex]Notice that the denominator of the first fraction is 5 and the denominator of the second fraction is 10.
The steps to find the a Common denominator are shown below:
1. Descompose 5 and 10 into their Prime factors:
[tex]\begin{gathered} 5=5 \\ 10=2\cdot5 \end{gathered}[/tex]2. In this case, you need to choose 5, because it is the common one. It will be the Common denominator of the fractions.
3. Divide the original denominator of the first fraction by the Common denominator 5. Multiply the the numerator by the result. Then:
[tex]\frac{2}{5}=\frac{2\cdot1}{5}=\frac{2}{5}[/tex]4. Apply the procedure explained in step 3 to the second fraction:
[tex]\frac{3}{10}=\frac{3\cdot2}{5}=\frac{6}{5}[/tex]5. You can identify that you can also get a common denominator multiplying the denominators and the numerators of both fractions by
The answer is: Option C.
In the diagram below of triangle NPQ, R is a midpoint of NP and S is a midpoint of PQ. If RS 15 - x, and NQ = 9x - 36, what is the measure of NQ?
The triangle midpoint theorem is as stated above.
In our case,
RS is joining the midpoints of NP and PQ.
Hence by the triangle midpoint theorem,
[tex]\begin{gathered} RS\parallel NQ\text{ and } \\ RS=\frac{1}{2}NQ \end{gathered}[/tex]Therefore,
triangle PRS is similar to triangle PNQ.
This means that the ratios of their corresponding sides are equal.
[tex]\frac{NQ}{RS}=\frac{NP}{RP}[/tex]Since R is the midpoint of NP then
[tex]\frac{NP}{RP}=2[/tex]Therefore,
[tex]\begin{gathered} \frac{NQ}{RS}=2 \\ \Rightarrow NQ=2RS \end{gathered}[/tex]Hence,
[tex]\begin{gathered} 9x-36=2(15-x) \\ \Rightarrow9x-36=30-2x \\ \Rightarrow9x+2x=30+36 \\ \Rightarrow11x=66 \\ \Rightarrow x=\frac{66}{11}=6 \end{gathered}[/tex][tex]\begin{gathered} \text{ Therefore,} \\ NQ=9x-36 \\ \text{gives} \\ NQ=9(6)-36=54-36=18 \end{gathered}[/tex]Hence the measure of NQ is 18
Please help me answer question 1,2 and plot this graph
b: When x increases by 1, y increases 1 unit.
c. Apply the slope formula (m)
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]Replace with 2 points form the table:
For example:
Point 1 = (x1,y1)= (0,3)
Point 2= (x2,y2)= (1,4)
Replacing:
[tex]m=\frac{4-3}{1-0}=\frac{1}{1}=1[/tex]Slope = 1
It doesn't need to be written because x multiplied by 1 is equal to x.
Graph.
y=mx+b
y=x+3
Where :
b= y-intercept = 3( where the line crosses the y-axis)
m= slope=1
diana has gift box that is 11 inches long, 8 inches wide and 6 inchers she has a sheet of wrapping paper that is 4 feet long by 1 foot wide does she have enough wrapping paper to wrap the box? justify your anwser
For this problem we need the paper sand to be enough to cover the surface of the box.
now we calculate the surface area of the box finding the area of each face
Surface
frontal face and bottom
the area is
[tex]\begin{gathered} A=6\times11 \\ A=66 \end{gathered}[/tex]the area of frontal face and bottom is
[tex]\begin{gathered} A=66+66 \\ A=132 \end{gathered}[/tex]left and right face
the area is
[tex]\begin{gathered} A=6\times8 \\ A=48 \end{gathered}[/tex]area of both sides
[tex]\begin{gathered} A=48+48 \\ A=96 \end{gathered}[/tex]upper and lower face
[tex]\begin{gathered} A=8\times11 \\ A=88 \end{gathered}[/tex]and the are of both face is
[tex]\begin{gathered} A=88+88 \\ A=176 \end{gathered}[/tex]Total Surface is the sum of the area of all faces
[tex]\begin{gathered} S=132+96+176 \\ S=404 \end{gathered}[/tex]Total surface of the box is 404 squre inches
Area of the paper
first we change the feet per inches to do the comparison with the surface area of the bos
[tex]\begin{gathered} 4ft\times12=48in \\ 1ft\times12=12in \end{gathered}[/tex]the paper is
and the area of the paper is
[tex]\begin{gathered} A=12\times48 \\ A=576 \end{gathered}[/tex]the area of the paper is 576square inches
[tex]576>404[/tex]the are of the paper is greater than the suface area of the box, the paper will be enough
(c) Does f (x) have any holes? If so, where are they? (just the x-coordinate is suffi- cient)(d) Does f (x) have any x-intercepts? If so, what are they?
f(x) is not defined where the term of the denominator is zero.
This happens when x = 4, x = -5 or x = -1
The x-intercepts is the points where f(x) = 0
this happens when x = -7 and x = 3
Notice that x = -1 can't be a x-intercept because the function is not defined at this point.
Find the volume of the figure. Use 3.14 for ñ If necessary, round your answer to the nearest tenth.
The given figure is a cone. The formula for calculating the volume of a cone is expressed as
Volume = 1/3 x pi x radius^2 x height
From the information given,
radius = 6.5
height = 14
pi = 3.14
By substituting these values into the formula, we have
Volume = 1/3 x 3.14 x 6.5^2 x 14
Volume = 619.1 m^3
The angle of elevation and the angle of depression are congruent because they areA)Corresponding AnglesB)Alternate Interior AnglesC)Alternate Exterior AnglesD)Vertical Angles
Given:
There are given the statement:
The angle of elevation and the angle of depression are congruent:
Explanation:
According to the concept:
The angle of elevation and the angle of depression are congruent because they belong from an alternate interior angle.
Final answer:
Hence, the correct option is B.
Martin is 6 years old when his sister Cassandra is 3 years old. How old will Martin be when Cassandra is 6 years old?
Explanation:
Martin's age = 6 years old
Casandra's age = 3 years old
Difference in their age = 6 - 3
Difference in their age = 3
If f(x) = 3x4 + 2x3 – X + 15,what would be the list ofpossible rational roots?a) + 1, 5, 1,3,5,15b) +1,3,5,15c) }, 1, 3, 5, 15d) 1, 2, 3, 6, 9, 18
I need help please, find the distance between (8 ,6) and (3 -6)
Answer:
distance = 13
Explanation:
The distance between two points (x1, y1) and (x2, y2) can be calculated as
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Replacing (x1, y1) = (8, 6) and (x2, y2) = (3, -6), we get that the distance between these points is
[tex]\begin{gathered} d=\sqrt{(3-8)^2+(-6-6)^2} \\ \\ d=\sqrt{(-5)^2+(-12)^2} \\ \\ d=\sqrt{25+144} \\ \\ d=\sqrt{169} \\ \\ d=13 \end{gathered}[/tex]Therefore, the distance between the points is 13.
Marissa can plant 10 seeds in 1/5 hour. she divides to find the number of seeds she can plant per hour but she makes a mistake
Marissa can plant 10 seeds in 1/5 hour
Then averagely, she will plant 1 seed in
[tex]undefined[/tex]The diagonal of the figure Below represent the support beams for a patio covering.What IS the length of each support beam ? Given 30, and 10 yards
Since all the sides of the figure have the same length, then the figure is a rhombus. Then, its diagonals intersect at an angle of 90°.
Let O be the intersection of the diagonals of the rhombus. Notice that the triangle EOA is a right triangle. Since the side EA is the hypotenuse of the triangle, then, recalling the trigonometric functions:
[tex]\begin{gathered} \cos (30)=\frac{EO}{EA} \\ \sin (30)=\frac{OA}{EA} \end{gathered}[/tex]Use this information to solve for the segments EO and OA:
[tex]\begin{gathered} EO=EA\cdot\cos (30) \\ =10\cdot\frac{\sqrt[]{3}}{2} \\ =5\cdot\sqrt[]{3} \end{gathered}[/tex][tex]\begin{gathered} OA=EA\cdot\sin (30) \\ =10\cdot\frac{1}{2} \\ =5 \end{gathered}[/tex]Since the diagonal EM is twice the segment EO and the diagonal BA is twice the segment OA, then the lengths of the diagonals are:
[tex]\begin{gathered} BA=10 \\ EM=10\cdot\sqrt[]{3} \end{gathered}[/tex]Therefore, the answer is:
[tex]10\text{ yards and }10\cdot\sqrt[]{3}\text{ yards}[/tex]You randomly draw a marble, put it back, and then randomly draw a marble.What is the probability of drawing a yellow marble and then drawing a green marble? Write answer as a fraction.
Given:
The total number of marbles =7.
The number of yellow marbles = 2.
The number of green marbles =2.
The marbles are replaced after being drawn.
To find:
We need to find the probability of drawing a yellow marble and then drawing a green marble.
Explanation:
The probability of drawing yellow marble P(Y).
[tex]P(Y)=\frac{The\text{ number of yellow marbles}}{The\text{ total number of marbles}}[/tex][tex]P(Y)=\frac{2}{7}[/tex]The probability of drawing green marble P(G).
[tex]P(G)=\frac{The\text{ number of gr}een\text{ marbles}}{The\text{ total number of marbles}}[/tex][tex]P(G)=\frac{2}{7}[/tex]The probability of drawing a yellow marble and then drawing a green marble is
[tex]=P(Y)\times P(G)[/tex][tex]=\frac{2}{7}\times\frac{2}{7}[/tex][tex]=\frac{4}{49}[/tex]Final answer:
The probability of drawing a yellow marble and then drawing a green marble is 4/49.
A rain drop hitting a lake makes a circular ripple. If the radius, in inches, grows as a function of time in minutes according to r(t)=15√t+2, find the area of the ripple as a function of time. Find the area of the ripple at t=2 .
FiThe radius, in inches, grows as a function of time in minutes according to:
[tex]r(t)=15\sqrt{t+2}[/tex]We know that the area of a circle is given by:
[tex]A=\pi r^2[/tex]Where r is the radius of the circle. Then, using r(t) in this equation:
[tex]\begin{gathered} A(t)=\pi\cdot\lbrack r(t)\rbrack^2=\pi\lbrack15\sqrt{t+2}\rbrack^2 \\ \\ \therefore A(t)=225\pi(t+2) \end{gathered}[/tex]Finally, we evaluate this function for t = 2:
[tex]\begin{gathered} A(2)=225\pi(2+2)=225\pi(4) \\ \\ \therefore A(2)=900\pi\text{ in}^2 \end{gathered}[/tex]What is the diameter of a circle with circumference 24 pi ft?
Answer:
24 ft
Explanation:
The circumference of a circle is equal to:
[tex]C=d\cdot\pi[/tex]Where d is the diameter of the circle. So, replacing c by 24π feet, we get:
[tex]24\pi=d\cdot\pi[/tex]Dividing both sides by π, we get:
[tex]\begin{gathered} \frac{24\pi}{\pi}=\frac{d\cdot\pi}{\pi} \\ 24=d \end{gathered}[/tex]Therefore, the diameter is 24 ft
I'm using goformative to do my work, I have number 13 answer right but the rest show my answers incorrect, I will appreciate if you can help me with my question I will paste the image of the question I have.
Firstly, we will have to make a representation of the angle
We have this as follows;
As we can see, alpha added to theta is 180 degrees
Firstly, by the use of Pythagoras' theorem, we can get the value of r
r faces the right angle, and that makes it the hypotenuse
According to the theorem, the square of r, the hypotenuse equals the sum of the squares of the two other sides
Thus, we have it that;
[tex]\begin{gathered} r^2=(-2)^2+4^2 \\ r^2\text{ = 4 + 16} \\ r^2\text{ = 20} \\ r\text{ = }\sqrt[]{20} \\ r\text{ = 2}\sqrt[]{5} \end{gathered}[/tex]From here, we can proceed to get the individual trigonometric ratios
a) Sine
This is the ratio of the opposite to the hypotenuse
On the second quadrant, the value of sine is positive
Thus, we have it that;
[tex]\begin{gathered} \sin \text{ }\alpha\text{ = }\frac{4}{2\sqrt[]{5}} \\ \alpha\text{ = }\sin ^{-1}(\frac{4}{2\sqrt[]{5}}) \\ \alpha\text{ = 63.43} \\ \theta\text{ = 180-63.43} \\ \theta\text{ = 116.57} \\ \sin \text{ 116.57 = }\frac{4}{2\sqrt[]{5}\text{ }}=\text{ }\frac{4\sqrt[]{5}}{10}\text{ = }\frac{2\sqrt[]{5}}{5} \\ \\ \sin \text{ }\theta\text{ = }\frac{2\sqrt[]{5}}{5} \end{gathered}[/tex]b) cosine
The cosine of an angle is the ratio of the adjacent to the hypotenuse
Mathematically, we know that;
[tex]\begin{gathered} \cos ^2\theta+sin^2\theta\text{ = 1} \\ \cos ^2\theta=1-sin^2\theta \\ \cos ^2\theta\text{ = 1 - (}\frac{2\sqrt[]{5}}{5})^2 \\ \\ \cos ^2\theta\text{ = 1- }\frac{20}{25} \\ \\ \cos ^2\theta\text{ = }\frac{5}{25} \\ \cos ^2\theta\text{ = }\frac{1}{5} \\ \\ \cos \text{ }\theta\text{ = }\sqrt[]{\frac{1}{5}} \\ \\ \cos \text{ }\theta\text{ = -}\frac{\sqrt[]{5}}{5} \end{gathered}[/tex]We choose the negative value for the cosine since cosine is negative on the second quadrant
c) Tan
The tan of an angle is the ratio of the opposite to the adjacent
Also, by dividing the sine of an angle by the cosine of the same angle, we can get the tan of the angle
Thus, we have it that;
[tex]\begin{gathered} \text{Tan }\theta\text{ = }\frac{\sin \text{ }\theta}{\cos \text{ }\theta} \\ \\ \text{Tan }\theta\text{ = }\frac{\frac{2\sqrt[]{5}}{5}}{\frac{-\sqrt[]{5}}{5}}\text{ = }\frac{2\sqrt[]{5}}{5}\times\frac{5}{-\sqrt[]{5}}\text{ = -2} \end{gathered}[/tex]d) cosec theta
The cosec of an angle is the multiplicative inverse of the sine
Mathematically;
[tex]\begin{gathered} co\sec \theta\text{ = }\frac{1}{\sin \text{ }\theta} \\ \\ co\sec \text{ }\theta\text{ = }\frac{1}{\frac{2\sqrt[]{5}}{5}}\text{ = }\frac{5}{2\sqrt[]{5}}\text{ = }\frac{5\sqrt[]{5}}{10}\text{ = }\frac{\sqrt[]{5}}{2} \end{gathered}[/tex]e) sec theta
The sec of an angle is the multiplicative inverse of the cosine of the angle
Thus, we have it that;
[tex]\text{sec }\theta\text{ = }\frac{1}{\cos \text{ }\theta}\text{ = }\frac{1}{-\frac{\sqrt[]{5}}{5}}\text{ = -}\frac{5}{\sqrt[]{5}}\text{ = -}\frac{5\sqrt[]{5}}{5}\text{ = -}\sqrt[]{5}[/tex]f) cot theta
The cot of an angle is the multiplicative angle of the tan
Thus, we have it that;
[tex]\begin{gathered} \cot \text{ }\theta\text{ = }\frac{1}{\tan \text{ }\theta} \\ \\ \cot \text{ }\theta\text{ = }\frac{1}{-2}\text{ = -}\frac{1}{2} \end{gathered}[/tex]I understand this, but, I’m not having the best of luck with this problem, I need a quick breakdown please.
Answer:
The period of the given graph is approximately 13 hours;
[tex]13[/tex]Explanation:
Given the graph in the attached image.
The period of a graph is the horizontal distance between two points over which a complete cycle occurs;
As shown in the figure below;
The two lowest points are at points;
[tex]\begin{gathered} (6,2.02) \\ \text{and} \\ (19,2.00) \end{gathered}[/tex]The period will be the horizontal distance between the two points;
[tex]\begin{gathered} P\approx19-6 \\ P\approx13 \end{gathered}[/tex]Therefore, the period of the given graph is approximately;
[tex]13[/tex]The table shows the busiest airports, shipping ports, and rapid rail systems in the United States. Suppose you are doing a report in which you have to research one entry from each column. You have no preference for any choices over any other choices. What is the probability that you would select Chicago O’Hare Intl. Airport, the port of Houston, Texas, and the Boston MBTA?
Ok, so
First of all, we're going to research one entry from each column.
In the first column, we want to know what's the probabili
Solve the following system of equations and state whether the system is dependent, independent, or inconsistent.4x+3y=12And4x-3y=12
Given:
[tex]\begin{gathered} 4x+3y=12 \\ 4x-3y=12 \end{gathered}[/tex]Required:
To solve the system of equation using graph and to state whether the system is dependent, independent, or inconsistent.
Explanation:
Consider the equation
[tex]4x+3y=12[/tex]When x=0,
[tex]\begin{gathered} 0+3y=12 \\ 3y=12 \\ y=\frac{12}{3} \\ y=4 \end{gathered}[/tex]When x=3,
[tex]\begin{gathered} 12+3y=12 \\ 3y=12-12 \\ 3y=0 \\ y=0 \end{gathered}[/tex]Now consider the equation
[tex]4x-3y=12[/tex]When x=0,
[tex]\begin{gathered} 0-3y=12 \\ -3y=12 \\ y=-\frac{12}{3} \\ y=-4 \end{gathered}[/tex]When x= 3,
[tex]\begin{gathered} 12-3y=12 \\ -3y=12-12 \\ -3y=0 \\ y=0 \end{gathered}[/tex]The graph of the given system of equation is,
The blue graph is graph of 4x+3y=12 and the black graph is graph of
4x-3y=12.
The two line crosses at the point (3,0).
Therefore the solution is
[tex]\begin{gathered} x=3 \\ y=0 \end{gathered}[/tex]Here the solution is one.
Therefore the consistent system has exactly one solution, it is independent .
Final Answer:
The solution of the given system of equation is
[tex]\begin{gathered} x=3 \\ y=0 \end{gathered}[/tex]The consistent system has exactly one solution, it is independent .
there are 30 votes for skating rink and 13 volts per bowling alley what is the ratio of number of votes for skating to the number of votes for bowling
Let's begin by listing out the given information:
Skating rink = 30 votes
Volts per bowling alley = 13
The ratio of the number of votes for skating to the number of votes for bowling is:
[tex]30\colon13[/tex]can you help me plot these points on the number line
To plot these numbers on the given umber line, we need to identify where they would be on the number line
The number 2 3/8 is between 2 and 3 while the number 1 3/4 is between the 1 and 2
Now, we need to identify each of the small points between the numbers
Between two numbers on the line, we can count 7 small lines and a total of 8 spaces
Now to get what each of the small lines represent, we need to divide 1 by the number of spaces.
What this mean is that each of this small numbers between each of the big digits represent the fraction 1/8
Now, recall, we know that 2 3/8 is between 2 and 3, to identify the exact place to position it, divide the fractional part by 1/8
What this mean is that we have 3/8 divided by 1/8 = 3/8 * 8/1 = 3
So what this means is that the number 2 3/8 is on the third small line after 2 (between 2 and 3)
For 1 3/4, we know that the number is between 3 and 4
To know thw exact spot, we find the division of the fractional part by 1/8
Mathematically, that will be 3/4 divided by 1/8 = 3/4 * 8/1 = 6
So this mean it is on the sixth small line after 1 (between 1 and 2)
The graph of =yfx is shown below.Draw the graph of =y12fx.
Multiplying f(x) by 1/2 meant that the function is being compressed by a factor of 1/2. This means that the function gets closer to the x-axis.
Based on the graph, the slope of the linear function is -1/2. See the illustration below to see why.
If we multiply the slope -1/2 by the factor 1/2, the slope changes to -1/4.
Also, the y-intercept that is at y = -3 after multiplying by a factor of 1/2, the y-intercept changes to -1.5.
Hence, the graph of y = 1/2f(x) will have a y-intercept at y = -1.5 and has a slope of -1/4. The graph of y = 1/2f(x) is shown below. (blue line)
The function h(t) = -16t(t - 2) + 24 models the height h, in feet, of a ball t seconds after it is thrown straight up into the air. What are the initial velocity and the initial height of the ball? O 16 ft/s: 32 ft 32 ft/s: 24 ft 24 ft/s: 32 ft 48 ft/s: 24 ft
Answer
Option B is correct.
Initial velocity = 32 ft/s
Initial height = 24 ft.
Explanation
The function gives us the function that models the height, h, in feet for the ball as a function of time, t, in seconds.
h(t) = -16t (t - 2) + 24
We are then asked to find the initial velocity and the initial height of the ball.
This means we find the velocity and the height of the ball at t = 0
Velocity is given as the first derivative of the height function
v = (dh/dt)
h(t) = -16t (t - 2) + 24
h(t) = -16t² + 32t + 24
v = (dh/dt) = -32t + 32
When t = 0
v = -32t + 32 = -32 (0) + 32 = 0 + 32 = 32 ft/s
Initial velocity = 32 ft/s
For the initial height, t = 0
h(t) = -16t (t - 2) + 24
h(t) = -16t² + 32t + 24
h(0) = -16(0²) + 32(0) + 24
h(0) = 0 + 0 + 24
h(0) = 24 ft
Initial height = 24 ft.
Hope this Helps!!!
HU Pon estos numeros en orden de menor a mayor: 5, 8,-1,-3. nine 8, 5, -3,-1 O O O 0 -1,3,5,8 0 -3, -1, 5,8
The given numbers are,
[tex]5,8,-1,-3[/tex]As we know, -3 < -1 < 5 < 8 therefore we can arrange the number in the order from least to the greatest as,
[tex]-3,-1,5,8[/tex]heather is six years younger than her husband ryan the sum of their ages is 5w how old is ryan a)23b)29c)31d)46
Bob works as a plumber he charges an initial fee of $45 and $32.50 an hour Bob was paid $207.50 for his last job how many hours did Bob work on his last job
We have the following:
Bob's earnings can be calculated with the following equation
[tex]B=45+32.5x[/tex]where x is the number of hours, they tell us that he made a profit of $ 207.50, we replace and solve for x
[tex]\begin{gathered} 207.5=45+32.5x \\ 32.5x=207.5-45 \\ x=\frac{162.5}{32.5} \\ x=5 \end{gathered}[/tex]Therefore, Bob worked a total of 5 hours
6 -7-6-5 4 5 6 기 7. I Which of these best represents the domain of f. F-3 5.5 ] All real numbers less than -3 or greater than 2
In this problem we have a quadratic function (vertical parabola open upward)
the domain is all real numbers
therefore
the answer is option GA Type I error is the mistake of ________ when it is actually true. rejecting the null hypothesisA study of the amount of time it takes a mechanic to rebuild the transmission for a 2010 Chevrolet Colorado shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 8.9 hours.
Question 2
Answer:
Explanation:
Let x be a random variable representing the mean amount of time it takes a mechanic to rebuild the transmission for a 2010 Chevrolet Colorado. Given that it is normally distributed, we would calculate the z score by applying the formula,
z = (x - μ)/σ/√n
where
μ is the population mean
x is the sample mean
σ is the population standard deviation
n is the sample size
From the information given,
n = 40
x = 8.9
μ = 8.4
σ = 1.8
Thus,
z = (8.9 - 8.4)/(1.8/√40) = 1.76
We want to calculate P(x < 8.9). The probability value corresponding to z = 1.76 from the normal distribution table is 0.9608
Thus, the probability that their mean rebuild time is less than 8.9 hours is 0.9608
Please help will mark Brainly
Answer:
A,B, D
Step-by-step explanation:
the slope is undefined since this line is vertical
and since it is vertical and endless it will have all y values
There is no y intercept since it’s off to the side of the y axis but there is an x intercept which is at -2 since that is the only x value on the line
Hopes this helps please mark brainliest
Answer: A,B,D
Step-by-step explanation:
It is B and D because the x intercept is -2 because since it is only x=-2 it is undefined slope because it can be any y number, but can only be x=-2 which gives you B and D
Mark me as brainliest!
Please help will mark brainlessness
Answer:
f(x) y-intercept: 7
f(x) x-intercept: -7/2 or -3.5
g(x) y-intercept: 21
g(x) x-intercept: -7/2 or -3.5
Step-by-step explanation:
The y-intercept of any function can be found, by substituting in 0 as x. The reason for this is because anywhere on the y-axis, the x-value will be equal to zero. So we know the x-value is going to be zero, we just need to solve for the y-value.
So to find the y-intercept of "g", we simply calculate g(0):\
[tex]g(0) = 3(2(0) + 7)\\\\g(0) = 3(7)\\\\g(0) = 21[/tex]
so the y-intercept of the function is 21. Now to find the y-intercept of f, we do the same thing:
[tex]f(0) = 2(0)+7\\\\f(0)=7[/tex]
Now to find the x-intercept, we use a similar method. Anywhere on the x-intercept, the y-value is zero, and the x-value may vary. In function notation, the f(x) and g(x) represent the y-value, so we simply substitute it as zero.
To find x-intercept of g, just set g(x) equal to zero:
[tex]0 = 3(2x+7)[/tex]
now from here, we usually would have two solutions. Since if one of the factors equals zero, then the entire thing is zero, regardless of the other value.
So let's set the factor (x+7) equal to zero: [tex]2x+7 = 0\implies 2x = -7\implies x=-\frac{7}{2}[/tex]
let's set 2 equal to zero: [tex]2=0[/tex], which is of course never true, so we only have the one solution of x = -7
To find the x-intercept of f, do the same process:
[tex]2x+7=0\implies 2x=-7\implies x=- \frac{7}{2}[/tex]
The volume of a cylinder is 603.2 cubic inches. If the cylinder has a height of 12 inches, what is the area of the base
Volume of a cylinder = base area x heigth
Volume = 603.2 in3
Height = 12 in
Replacing:
603.2 = base area x 12
603.2/12 = base area
Base area = 50.26 in2