Need help with this question
Answers
Given the following question:
[tex]f(x)=\frac{2x}{x-1}[/tex]Graph the following function:
To find the vertical asymptotes, trace a line vertically inbetween the function.
To find the horizontal do the same but as a horizontal line.
If x = 1 then the both lines will soon touch the vertical line which means the vertical asymptotes is 1. While horizontal if you draw a line y = 2 you will see that it is the same which means the horizontal asympototes is 2.
Which means your answer is the second option.
Related Questions
determine the volume of each rectangular or rectangle prism round to the nearest tenth if necessary
Answers
The volume of the triangular prism is given by:
[tex]\begin{gathered} V=\frac{1}{2}b\cdot h\cdot l \\ \text{Where:} \\ b=\text{base}=7.2 \\ h=\text{height}=9 \\ l=\text{length}=3 \\ V=\frac{1}{2}\cdot7.2\cdot9\cdot3 \\ V=97.2m^3 \end{gathered}[/tex]Using the domain {-2,-1,0,1,2} draw the graph f(x) = -3 if x<0, -1 if x=0, xif x>0
Answers
First, we compute f(x) for each x in the domain:
[tex]\begin{gathered} f(-2)=-3, \\ f(-1)=-3, \\ f(0)=-1, \\ f(1)=1, \\ f(2)=2. \end{gathered}[/tex]Therefore, the graph of the function is as follows:
The sides of a triangle measure 4,6., and 7. If the shortest side of a similar friangle is 12, what is the perimeter of the larger triangle?
Answers
The perimeter of the larger triangle is 51
Here, we want to calculate the perimeter of the larger triangle
From the smaller triangle, we can see that its shortest side is 4
The shortest side of the larger triangle is 12
This shows that the scale of the larger to the smaller is 3 to 1
Mathematically, what this means is that, by multiplying the length of the smaller triangle by 3, we can get the sides of the larger
Hence, what we have at this point is that the sides of the larger triangle are 12 by 18 by 21
Mathematically, the perimeter of a triangle can be calculated by adding the length of the sides together
With respect to this question, the perimeter of the larger triangle will be;
12 + 18 + 21 = 51
Hi there, I am a little lost on how to figure this out.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
triangles diagram
Step 02:
We must analyze the figure to find the solution.
triangle ABC:
∠ A + ∠ B + ∠ C = 180°
∠ A + 30 + 90 = 180
∠ A = 180 - 90 - 30 = 60
∠ A = 60°
BC:
[tex]\begin{gathered} cos\text{ 30 = adjacent / hypotenuse} \\ \\ cos\text{ 30 = }\frac{BC}{16\text{ }\sqrt{3}} \end{gathered}[/tex]BC = 24
AC:
AC = opposite
[tex]\begin{gathered} sin\text{ B = opposite / hypotenuse} \\ \\ sin\text{ 30 = }\frac{AC}{16\sqrt{3}} \\ \\ 16\sqrt{3}*sin\text{ 30 = AC} \\ \\ 13.86\text{ = AC} \end{gathered}[/tex]triangle ACD:
opposite = BD
adjacent = AC
BD:
[tex]\begin{gathered} tan\text{ 30 = opposite / adjacent } \\ \\ tan\text{ 30 = }\frac{DC}{13.86} \\ \\ 13.86\text{ * tan 30 = DC} \\ \\ \text{8 = DC} \\ \\ BD\text{ = 24 - 8 = 16} \end{gathered}[/tex]The answer is:
BD = 16
I need help with this problem from the calculus portion on my ACT prep guide
Answers
Given a series, the ratio test implies finding the following limit:
[tex]\lim _{n\to\infty}\lvert\frac{a_{n+1}}{a_n}\rvert=r[/tex]If r<1 then the series converges, if r>1 the series diverges and if r=1 the test is inconclusive and we can't assure if the series converges or diverges. So let's see the terms in this limit:
[tex]\begin{gathered} a_n=\frac{2^n}{n5^{n+1}} \\ a_{n+1}=\frac{2^{n+1}}{(n+1)5^{n+2}} \end{gathered}[/tex]Then the limit is:
[tex]\lim _{n\to\infty}\lvert\frac{a_{n+1}}{a_n}\rvert=\lim _{n\to\infty}\lvert\frac{n5^{n+1}}{2^n}\cdot\frac{2^{n+1}}{\mleft(n+1\mright)5^{n+2}}\rvert=\lim _{n\to\infty}\lvert\frac{2^{n+1}}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^{n+1}}{5^{n+2}}\rvert[/tex]We can simplify the expressions inside the absolute value:
[tex]\begin{gathered} \lim _{n\to\infty}\lvert\frac{2^{n+1}}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^{n+1}}{5^{n+2}}\rvert=\lim _{n\to\infty}\lvert\frac{2^n\cdot2}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^n\cdot5}{5^n\cdot5\cdot5}\rvert \\ \lim _{n\to\infty}\lvert\frac{2^n\cdot2}{2^n}\cdot\frac{n}{n+1}\cdot\frac{5^n\cdot5}{5^n\cdot5\cdot5}\rvert=\lim _{n\to\infty}\lvert2\cdot\frac{n}{n+1}\cdot\frac{1}{5}\rvert \\ \lim _{n\to\infty}\lvert2\cdot\frac{n}{n+1}\cdot\frac{1}{5}\rvert=\lim _{n\to\infty}\lvert\frac{2}{5}\cdot\frac{n}{n+1}\rvert \end{gathered}[/tex]Since none of the terms inside the absolute value can be negative we can write this with out it:
[tex]\lim _{n\to\infty}\lvert\frac{2}{5}\cdot\frac{n}{n+1}\rvert=\lim _{n\to\infty}\frac{2}{5}\cdot\frac{n}{n+1}[/tex]Now let's re-writte n/(n+1):
[tex]\frac{n}{n+1}=\frac{n}{n\cdot(1+\frac{1}{n})}=\frac{1}{1+\frac{1}{n}}[/tex]Then the limit we have to find is:
[tex]\lim _{n\to\infty}\frac{2}{5}\cdot\frac{n}{n+1}=\lim _{n\to\infty}\frac{2}{5}\cdot\frac{1}{1+\frac{1}{n}}[/tex]Note that the limit of 1/n when n tends to infinite is 0 so we get:
[tex]\lim _{n\to\infty}\frac{2}{5}\cdot\frac{1}{1+\frac{1}{n}}=\frac{2}{5}\cdot\frac{1}{1+0}=\frac{2}{5}=0.4[/tex]So from the test ratio r=0.4 and the series converges. Then the answer is the second option.
find the distance between the two points. round Your solution to w decimal points
Answers
Explanation
Step 1
the distance between two points is given by
[tex]\begin{gathered} \text{distance AB=}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where } \\ (x_1,y_1)^{}and(x_2,y_2)\text{ are the coordinates of the points A and B} \end{gathered}[/tex]Step 2
look in the graph the coordinate of A and B
Let
A(-5,-2)
B(4,1)
Step 3
replace,
[tex]\begin{gathered} \text{distance AB=}\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{ AB=}\sqrt[]{(4-(-5))^2+(1-(-2))^2} \\ \text{AB=}\sqrt[]{(9)^2+(3)^2} \\ \text{AB=}\sqrt[]{90} \\ \end{gathered}[/tex]rouded 9.48
I hope this helps you
Please solve, fill in the blank for each (a) through (d)
Answers
We are given the following function:
[tex]f(x)=\frac{x}{x-8},g(x)=-\frac{1}{x}[/tex]Part A. We are asked to determine the following:
[tex]f\circ g[/tex]This means the composition of the function "f" and "g". To do that we will use the following equivalence:
[tex](f\circ g)(x)=f(g(x))[/tex]This means that we will substitute the value of "x" from function "f" by the function "g", like this:
[tex]f(g(x))=\frac{-\frac{1}{x}}{-\frac{1}{x}-8}[/tex]Now, we simplify the fraction:
[tex]f(g(x))=\frac{1}{1+8x}[/tex]To determine the domain we must set the denominator to zero to determine the values of "x" for which the composition of the functions is undetermined:
[tex]1+8x=0[/tex]Now, we solve for "x". First, we subtract 1 from both sides:
[tex]8x=-1[/tex]Now, we divide both sides by 8:
[tex]x=-\frac{1}{8}[/tex]Therefore, the composition is undetermined at the point "x = -1/8". Therefore, the domain is:
[tex]D={}\lbrace x\parallel x<-\frac{1}{8},x>-\frac{1}{8}\rbrace[/tex]Part B. we are asked to determine the following:
[tex]g\circ f[/tex]This is equivalent to:
[tex](g\circ f)(x)=g(f(x))[/tex]This means that we will substitute the value of "x" from function "g" for the value of function "f", like this:
[tex]g(f(x))=-\frac{1}{\frac{x}{x-8}}[/tex]Now, we simplify the expression:
[tex]g(f(x))=-\frac{x-8}{x}[/tex]To determine the domain we set the denominator to zero:
[tex]x=0[/tex]Therefore, the function is undetermined at "x = 0". This means that the domain is the values of "x" that do not include the value of "x = 0":
[tex]D=\lbrace x\parallel x>0,x<0\rbrace[/tex]Part C. We are asked to determine:
[tex]f\circ f[/tex]This is equivalent to:
[tex](f\circ f)(x)=f(f(x))[/tex]Now, we substitute the value of "x":
[tex]f(f(x))=\frac{\frac{x}{x-8}}{\frac{x}{x-8}-8}[/tex]Now, we multiply the numerator and denominator by "x - 8":
[tex]f(f(x))=\frac{x}{x-8(x-8)}[/tex]Applying the distributive property and adding like terms we get:
[tex]f(f(x))=\frac{x}{x-8x+64}=\frac{x}{-7x+64}[/tex]Now, we set the denominator to zero to determine the domain:
[tex]-7x+64=0[/tex]Now, we subtract 64 from both sides:
[tex]-7x=-64[/tex]Now, we divide both sides by -7:
[tex]x=\frac{64}{7}[/tex]Therefore, the domain does not include the value of "x = 64/7". Therefore, the domain is:
[tex]D=\lbrace x\parallel x<\frac{64}{7},x>\frac{64}{7}\text{ \textbraceright}[/tex]Part D. We are asked to determine:
[tex](g\circ g)(x)=g(g(x))[/tex]Substituting the value of "g(x)" in "g(x)" we get:
[tex]g(g(x))=-\frac{1}{-\frac{1}{x}}[/tex]Simplifying we get:
[tex]g(g(x))=x[/tex]To determine the domain we need to have into account that the function is a polynomial and therefore, is not undetermined at any point. This means that the domain is all the real numbers.
AD and AC are tangent to the circle. Find m
Answers
SOLUTION:
We use the intersecting tangents theorem;
Thus;
[tex]\begin{gathered} m\angle DAC+130=180 \\ m\angle DAC=180-130 \\ m\angle DAC=50^o \end{gathered}[/tex]Thus,
[tex]m\angle DAC=50^o[/tex]Hi it’s RoseI’m having trouble on this problem from my prep guide, need help solving it
Answers
The Equation of a Circle
If a circle has its center at the point (h, k) and has a radius r, the equation of the circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]We are only given the endpoints of the diameter of the circle (3, -2) and (-5, 8). We need to find its center and radius.
These facts will help us to find both parameters:
* The diameter passes through the center of the circle.
* The center of the circle is the midpoint of the diameter.
* The radius of the circle is half the length of the diameter.
The midpoint of the diameter can be calculated as:
[tex]\begin{gathered} x_m=\frac{3-5}{2} \\ x_m=\frac{-2}{2} \\ x_m=-1 \end{gathered}[/tex][tex]\begin{gathered} y_m=\frac{8-2}{2} \\ y_m=\frac{6}{2} \\ y_m=3 \end{gathered}[/tex]The coordinates of the midpoint are (-1, 3) and it happens to be the center of the circle, thus h = -1 and k = 3.
To find the radius, we need to calculate the distance from the center to any of the endpoints. Let's use the points (-1, 3) and (3, -2) and use the formula of the distance:
[tex]\begin{gathered} r^2=(3+1)^2+(-2-3)^2 \\ r^2=16+25 \\ r^2=41 \end{gathered}[/tex]We don't need to calculate the value of r. Its square is enough to substitute in the general form of the circle to get:
[tex]\boxed{\mleft(x+1\mright)^2+\mleft(y-3\mright)^2=41}[/tex]For a standard normal distribution, find:P(1.81 < z < 2.14)
Answers
SOLUTION
From the question, we want to find
P(1.81 < z < 2.14)
Using the Zscore calculator, we have
P(1.81
Hence the answer is 0.0190 to 4 decimal places
in a bag, there are 11 red balls and 14 green balls. There are no other balls in the bag. what is the ratio of green balls to the total number of balls in the bag? A. 11 to 25B. 11 to 14 C. 14 to 25 D. 14 to 11
Answers
Explanation:
In total, there are 11 + 14 = 25 balls in the bag. The ratio of green balls to the total number of balls in the bag is 14 (green balls) to 25 (total number of balls).
Answer:
C. 14 to 25
Find the X and Y intercepts of the graph of the given equation3x+6y=54
Answers
Step 1
To find x-intercept, make x subject of the relation
3x + 6y = 54
3x = -6y + 54
Divide through by 3
[tex]\begin{gathered} \frac{3x}{3}\text{ = }\frac{-6y}{3}\text{ + }\frac{54}{3} \\ x\text{ = -2y + 18} \end{gathered}[/tex]Therefore x intercept from x = my + c
c is the intercept
Therefore, x intercept = 18
To find x-intercept, make x subject of the relation
3x + 6y = 54
6y = -3x + 54
Divide through by 6
[tex]\begin{gathered} \frac{6y}{6}\text{ = }\frac{-3x}{6}\text{ + }\frac{54}{6} \\ y\text{ = }\frac{-x}{2}\text{ + 9} \end{gathered}[/tex]Therefore y-intercept from y = mx + c
c is the intercept
Therefore, y-intercept = 9
the equation v=1/3 represents the volume of a cone where r is the radius of the cone
Answers
The cone has a height value of 7.01 cm
How to determine the height of the cone using the volume formula?From the question, we have the following parameters that can be used in our computation:
Formula: Volume, v = 1/3πr²h
The above formula represents the volume of a cone
Such that
V = Volume; R = Radius and H = Height
Also, we have
Volume, v = 66
Radius, r = 3
Recall that
v = 1/3πr²h
Multiply both sides by 3
So, we have the following equation
3v = πr²h
Divide both sides by πr²
So, we have the following equation
h = 3v/πr²
Substitute 66 for v and 3 for r
So, we have the following representation
h = 3 * 66/(3.14 * 3²)
Evaluate
So, we have the following equation
h = 7.01 cm
Hence, the height of the cone is 7.01 cm
Read more about volume at
https://brainly.com/question/463363
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Complete question
The equation v = 1/3πr²h represents the volume of a cone where r is the radius of the cone and h represents the height.
What is the height of a cone with a volume of 66 cubic centimetres and a base with radius of 3 centimetres
We will assume that the first month you open is February, so there are 4 weeks in your month. Write an equation showing your total cost, which includes the rent, utilities, bowls, cones, spoons, and employees. It is up to you to decide how many of the cones, bowls, spoons you need to order, so make sure to include that information. Each pack of spoons, cones, or cups cost 5$ each. Remember that each pack of spoons has 100 spoons, each pack of cones has 60 cones, and each pack of cup has 80 cups. Next, determine how much you would charge for a small, medium, and large (assume that sizes are are the same for cones and bowls.) The table shows all of your orders for the month. Calculate how much you made in total sales. Finally, using your calculations from your total cost as well as your sales, figure out how much money you made your first month.
Answers
ANSWER
You made a total of $24,910 from your first month
STEP-BY-STEP EXPLANATION
Step 1: Equation showing the Total Cost
[tex]\text{Total Cost = Rent }+\text{ Utilities + Total Cost of Bowls +Total Cost of Cones+Total Cost of Cups+Total Cost of Spoons + Total Cost of Employees.}[/tex]Step 2: Table showing all the orders for the month
Step 3: Determine how much to charge for small, medium and large sizes.
Recall from the question that each pack of cones, bowls, spoons and cups costs $5 each.
Now, let's determine how much to charge.
Let's charge $7 for small sizes, $8 for medium sizes and $9 for large sizes.
Step 4: Calculate the total sales for the month
Cone = ($7 x 300) + ($8 x 800) + ($9 x 200) = $2100 + $6400 + $1800 = $10,300
Bowl= ($7 x 700) + ($8 x 1100) + ($9 x 600) = $19,100
Spoon = ($7 x 900) + ($8 x 700) + ($9 x 800) = $19,100
Cup= ($7 x 1000) + ($8 x 600) + ($9 x 900) = $19,900
Total sales = Total Cone + Total Bowl + Total Spoon + Total cup
Total sales = $10,300 + $19,100 + $19,100 + $19,900 = $68,400
Step 5: Determine the Total Cost
Total Cone = $5x(300+800+200) = $6,500
Total Bowl = $5x(700+1100+600) = $12,000
Total Spoon = $5x(900+700+800) = $12,000
Total Cup= $5x(1000+600+900) = $12,500
Let's assume the rent, utilities and employees.
Rent = $100
Utilities = $90
Employees = $300
Total Cost = $6,500 + $12,000 + $12,000 + $12,500 + $100 + $90 + $300 = $43,490.
Step 6: Determine how much you made
To determine the profit, subtract the total cost from the total sales.
Profit = Total Sales - Total Cost = $68,400 - $43,490 = $24,910.
Hence, you made a total of $24,910 from your first month.
erin has $50 she wants to purchase a cell phone ($20) and spend the rest on music CD's. each music CD costs $8. write an inequality for the number of music CD's she can purchase
Answers
Given:
Total Amount she has = $50
Amount she wants to spend on cellphone = $20
If she wants to spend the remaining amount on music CD's where each CD cost $8, let's write the inequality to represent this situation below.
Let C represent number of CDs
We have:
20 + 8C ≤ 50
Therefore, the inequality for the number of music CD's she can purchase is:
20 + 8C ≤ 50
ANSWER:
20 + 8C ≤ 50
Please help I’ll mark brainliest. Thank you :)
Answers
Answer:
Option B
Step-by-step explanation:
If it was a single reflection, it could not have be translated too.
Please actually mark me brainliest :)
8 + 4x > 12solve inequality
Answers
You have the following inequality:
8 + 4x > 12
in order to solve the previous inequality, proceed as follow:
8 + 4x > 12 subtract 8 both sides
4x > 12 - 8
4x > 4 divide by 4 both sides
x > 1
Hence, the solution to the given inequality is x > 1
part b: what is the apparent solution to the system of equations in the graph
Answers
Part B:
From the garph given, the solution to the system of equations will be the point where both lines intersect (where they meet).
The point of intersection is:
(x, y) ==> (2, 1)
Thus, we have the solution to the system of equations in the graph:
x = 2, y = 1
Part C:
Let's find the equation for both lines on the graph.
Use the slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept
For line 1:
Take the points:
(x1, y1) ==> (4, 0)
(x2, y2) ==> (0, 2)
Find the slope using the slope formula:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \\ m=\frac{2-0}{0-4}=\frac{2}{-4}=-\frac{1}{2} \end{gathered}[/tex]The y-intercept (b) is = 2
The slope(m) is = -½
Thus the equation of line 1 is:
y = -½x + 2
For line 2:
Take the points:
(x1, y1) ==> (0, -5)
(x2, y2) ==> (2, 1)
Find the slope:
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \\ m=\frac{1-(-5)}{2-0}=\frac{1+5}{2-0}=\frac{6}{2}=3 \end{gathered}[/tex]The slope(m) is 3
The y-intercept(b) is -5
Thus, the equation of line 2 is:
y = 3x - 5
Therefore, we have the system of equations:
[tex]\begin{gathered} y=-\frac{1}{2}x+2.............\mleft(equation1\mright) \\ \\ y=3x-5\ldots\ldots\ldots\ldots\ldots\text{.(equation 2)} \end{gathered}[/tex]Let's solve the system.
Eliminate the equal sides and combine the equations
We have:
-½x + 2 = 3x - 5
Subtract 2 from both sides:
-½x + 2 - 2 = 3x - 5 - 2
-½x = 3x - 7
Multiply all terms by 2:
[tex]\begin{gathered} -\frac{1}{2}x\ast2=3x(2)-7(2) \\ \\ -x=6x-14 \end{gathered}[/tex]Subtract 6x from both sides:
[tex]\begin{gathered} -x-6x=6x-6x-14 \\ \\ -7x=-14 \end{gathered}[/tex]Divide both sides by -7:
[tex]\begin{gathered} -\frac{7x}{-7}=\frac{-14}{-7} \\ \\ x=2 \end{gathered}[/tex]Substitute 2 for x in either of the equations.
Take equation 2:
y = 3x - 5
y = 3(2) - 5
y = 6 - 5
y = 1
Therefore, we have the solution to the system:
x = 2, y = 1
ANSWER:
x = 2, y = 1
Graph the system below and write its solution.1y=x+3- 2x + y = 6Note that you can also answer "No solution" or "Infinitely many" solutions.10+6-Solution:-10
Answers
EXPLANATION
The system of equations is given by the following expression:
(1) y = (1/2)x + 3
(2) -2x + y = 6
Substitute y= (1/2)x + 3
[tex]\begin{bmatrix}-2x+\frac{1}{2}x+3=6\end{bmatrix}[/tex]Simplifying:
[tex]-2x+\frac{1}{2}x+3=6[/tex]Adding similar elements:
[tex]-\frac{3}{2}x+3=6[/tex]Subtracting -3 to both sides:
[tex]-\frac{3}{2}x=6-3[/tex][tex]\mathrm{Multiply\: both\: sides\: by\: }2[/tex][tex]2\mleft(-\frac{3}{2}x\mright)=3\cdot\: 2[/tex]Simplify:
[tex]-3x=6[/tex]Divide both sides by -3:
[tex]\frac{-3x}{-3}=\frac{6}{-3}[/tex]Simplify:
[tex]x=-2[/tex][tex]\mathrm{For\: }y=\mleft(\frac{1}{2}\mright)x+3[/tex][tex]\mathrm{Substitute\: }x=-2[/tex][tex]y=\frac{1}{2}\mleft(-2\mright)+3[/tex]Remove parentheses: (-a) = -a
[tex]=-\frac{1}{2}\cdot\: 2+3[/tex][tex]\frac{1}{2}\cdot\: 2[/tex]Cancel the common factor:
[tex]=1[/tex][tex]=-1+3[/tex][tex]\mathrm{Add/Subtract\: the\: numbers\colon}\: -1+3=2[/tex]=2
y=2
[tex]\mathrm{The\: solutions\: to\: the\: system\: of\: equations\: are\colon}[/tex][tex]y=2,\: x=-2[/tex]What's the mean number of kernels per row in the sample of ears?
Answers
We know that the mean of a samples if given by:
[tex]\mu=\frac{x_1+x_2+\cdots+x_n}{n}[/tex]So we replace our data so:
[tex]\mu=\frac{49+52+48+52+54+51+53+\ldots+48+52}{20}[/tex]and we solve so:
[tex]\mu=\frac{1023}{20}=51.15[/tex]write the equation of a line perpendicular to the line that passes through the given point.[tex]y = - 5x - \frac{4}{3} [/tex](6,-4)
Answers
Answer:
The equation of a line perpendicular to the line that passes through the given point as;
[tex]y=\frac{x}{5}-\frac{26}{5}[/tex]Explanation:
Given that we want to find the eqution of the line perpendicular to the line equation below;
[tex]y=-5x-\frac{4}{3}[/tex]Whose slope is;
[tex]m_1=-5[/tex]For two lines to be perpendicular, the slope must follow the rule below;
[tex]\begin{gathered} m_1.m_2=-1 \\ m_2=\frac{-1}{m_1} \end{gathered}[/tex]Substituting the value of the given slope;
[tex]\begin{gathered} m_2=\frac{-1}{m_1}=\frac{-1}{-5} \\ m_2=\frac{1}{5} \end{gathered}[/tex]Now we have the slope of our line.
We can now derive the equation using the point-slope equation of line;
[tex]y-y_1=m(x-x_1)[/tex]With the given point;
[tex](x_1,y_1)=(6,-4)[/tex]Substituting the slope and the given point, we have;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-4)=\frac{1}{5}(x-6) \\ y+4=\frac{x}{5}-\frac{6}{5} \\ y=\frac{x}{5}-\frac{6}{5}-4 \\ y=\frac{x}{5}-\frac{26}{5} \end{gathered}[/tex]Therefore, we have the equation of a line perpendicular to the line that passes through the given point as;
[tex]y=\frac{x}{5}-\frac{26}{5}[/tex]Patricia needs atleast $200 to go to camp this summer. she has saved $60. She earns $5 per hour babysitting. Which inequality shows the number of hours Patricia needs to babysit,x, to earn enough money for her trip?
Answers
If x is the number of hours Patricia needs to babysit, the inequality is
[tex]savings+5x\ge200[/tex]Therefore, since she has already saved $60,
[tex]\Rightarrow60+5x\ge200[/tex]Thus, the inequality that models the question is 60+5x>=200
What equation models the line that goes through the point (12.3) and has a slope of
Answers
Explanation
when you know the slope and a passing point of the line you can use the slope-point equation:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ where\text{ mis the slope} \\ (x_1,y_1)\text{ is point from the line} \end{gathered}[/tex]then
Step 1
a)let
point(12,3)
slope=-1/3
replace and isolate y
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=-\frac{1}{3}(x-12_{}) \\ y-3=-\frac{1}{3}x+\frac{12}{3}) \\ y-3=-\frac{1}{3}x+4 \\ \text{add 3 in both sides} \\ y-3+3=-\frac{1}{3}x+4+3 \\ y=-\frac{1}{3}x+7 \end{gathered}[/tex]therefore, the answer is
[tex]D)y=-\frac{1}{3}x+7[/tex]I hope this helps you
Find the volume of each rectangular solid to solve the following problems. An open tin box is constructed from a rectangular plece of tin measuring 64 cm by 36 cm. Cutting 6 cm squares from each corner then folding up the sides makes the box. What is the volume of the box? It will help to make a sketch." A) 6,912 cubic cm B) 7,488 cubic cm C) 12,078 cubic cm D) 13,824 cubic cm
Answers
ANSWER
B) 7,488 cubic cm
EXPLANATION
We can make a diagram that will help understand this problem better:
The sides of the rectangle are 64cm and 36cm. It is said that we have to cut 6cm squares from each corner, therefore from those dimensions se have to subtract 12cm (6cm from each side). In the end, we have the box shown in the picture above. The volume is:
[tex]V=24cm\times52\operatorname{cm}\times6\operatorname{cm}=7,488\operatorname{cm}^3[/tex]How many per pounds of each kind should he use in the new mix round off the answer to nearest hundredth
Answers
ANSWER
14 pounds of $1.45 and 7 pounds of $2.20
STEP BY STEP EXPLANATION
Step 1:
let x be $1.45 per pound of coffee and
y be $2.20 per pound of coffee
He wants to mix a total of 21
The algebraic equation now is:
[tex]\begin{gathered} x\text{ + y = 21}\ldots\ldots\ldots\ldots..\ldots..\ldots\ldots..(1) \\ x\text{ = 21 - y }\ldots\ldots\ldots\ldots\ldots\ldots\ldots.\ldots.(2) \end{gathered}[/tex]Now, at the price of $1.70 per pound he will make $1.70 * 21 = $35.7
Step 2: Solve for y
[tex]\begin{gathered} 1.45\text{ x + 2.20 y = 35.7} \\ 1.45\text{ (21 - y) + 2.20 y = 35.7} \\ 30.45\text{ - 1.45y + 2.20y = 35.7} \\ 0.75\text{ y = 5.25} \\ y\text{ = }\frac{5.25}{0.75}\text{ = 7} \end{gathered}[/tex]Step 3: Solve for x
[tex]\begin{gathered} \text{from equation 2} \\ x\text{ = 21- 7} \\ x\text{ = 14} \end{gathered}[/tex]Hence, the grocer needs to use about 14 pounds of $1.45 and 7 pounds of $2.20 in the new mix.
Which inequality matches this graph?106A423-2f(x) > -(x + 2)2 - 5f(x) S-3(x + 2)2 - 5f(x) 2 3(x - 2)2 + 5f(x) <(x - 2)2 + 5
Answers
The inequality that matches this graph is
[tex]f(x)\ge3(x-2)^2+5[/tex]The qaudratic inequality has the output values "greater than or equal to" becaue of the shaded line of the parabola.
Also, the graph is shifted 5 units up on the y-axis.
The correct answer is the third one.
what is the average value 4+4+1+7=16
Answers
The sum of the terms is 16. The number if terms is 4. Then, the mean is:
[tex]\operatorname{mean}=\frac{16}{4}=4[/tex]Write the function rule g(x) after the given transformations of the graph of f(x) = 6x.1reflection in the x-axis; vertical compression by a factor of2g(x) = 0
Answers
SOLUTION
For a reflection in the x-axis,
[tex]\begin{gathered} g(x)=-f(x) \\ g(x)=-6x \end{gathered}[/tex]Now, for a vertical compression by a factor of
[tex]\frac{1}{2}[/tex]This becomes
[tex]\begin{gathered} g(x)=\frac{1}{2}\times-6x \\ g(x)=-3x \end{gathered}[/tex]Therefore, the answer = -3x
how can you tell if a graph is a tree by looking at the adjacency to matrix
Answers
Let's assume that a tree has N nodes, this means that this tree has N-1 edges.
For an adjacency matrix representing a tree, such will have 2(N-1) 1's, since each edge sets two bits in the matrix (with no 1's on the diagonal, since trees have no self-edges).
how do I get the total surface area of this solid?
Answers
Given:
[tex]\begin{gathered} \text{height(h)}=40\operatorname{cm} \\ \text{diameter(d)=28cm} \end{gathered}[/tex][tex]\begin{gathered} \text{radius(r)}=\frac{d}{2} \\ \text{radius(r)}=\frac{28}{2} \\ \text{radius(r)}=14\operatorname{cm} \end{gathered}[/tex][tex]\text{Total surface area=2}\pi(r)(h+r)[/tex][tex]\begin{gathered} \text{Total surface area=2}\times\frac{22}{7}\times14\times(40+14) \\ \text{Total surface area=}2\times22\times2\times54 \\ \text{Total surface area=}4752cm^2 \end{gathered}[/tex]