Answers
ANSWER
First point = (0, 3)
Second point = (1, -1)
Third point = (2, -5)
Graph:
EXPLANATION
To plot a graph using the slope and the y-intercept, simply apply the following rules:
1. Evaluate the function at x = 0, to determine the y-intercept which was (0,3) from the question
2. Determine the slope by finding the change in y divided by change in x. This was -4 according to the question. Which could also be written as -4/1; that is, rise divided by run
3. Now, from the value (0, 3) we got in step 1, we move down by 4 units and then to the right by 1 unit. This will lead us to the Second point of (1, -1). Also from this point, we move down by 4 units and then to the right by 1 unit to get to the Third point of (2, -5). You may decide to continue this pattern if you want more points.
4. Draw a straight line joining the 3 points together.
Related Questions
Find the domain and range of the relation Choose the correct domain below. a.) all real numbers b.) x=3c.) all real numbers except 3d.) none of the above Choose the correct range below a.) y=3b.)all real numbers except 3c.) all real numbers d.)none of the above
Answers
As this is a vertical line, its domain is just one point, x=3. And it's range is all the real numbers
Find the sum: - 5/8 + 1/3
Answers
Answer:
-7/24
Explanation:
Given the expression:
[tex]-\frac{5}{8}+\frac{1}{3}[/tex]Step 1: Find the lowest common multiple of the denominators.
The L.C.M. of 8 and 3 = 24
Step 2: Use the LCM to combine the fractions.
[tex]=\frac{-5(3)+1(8)}{24}[/tex]Step 3: Simplify:
[tex]\begin{gathered} =\frac{-15+8}{24} \\ =-\frac{7}{24} \end{gathered}[/tex]The result of the sum is -7/24.
5 Three pipes are connected to a water tank. One of the pipes can fill the tank in 30 minutes. The second pipe can fill it in 20 minutes. The third pipe can fill the tank in 40 minutes. How long will it take to fill the tank if all three pipes are opened together? If the slowest pipe is shut off after 3 minutes and the fastest pipe is shut off 3 minutes later, how long will it take the remaining open pipe to finish filling the tank?
Answers
Let's call the total volume of the tank as V. The rate each pipe fills the tank is given by the total volume of the tank divided by the amount of time it takes to fill the tank. Let's call the rate of the first pipe as r1, the rate of the second pipe as r2 and the rate of the third pipe as r3.
[tex]\begin{gathered} r_1=\frac{V}{30} \\ r_2=\frac{V}{20} \\ r_3=\frac{V}{40} \end{gathered}[/tex]The product between the rate and the time that has passed will give to us the fraction of the tank that has been filled. When we open the three pipes at once, we sum their rates. When the tank is filled, the product between the rate and the time passed must give the total volume of the tank, therefore, we have the following equation:
[tex]\begin{gathered} (\frac{V}{30}+\frac{V}{20}+\frac{V}{40})t=V \\ \frac{13V}{120}t=V \\ \frac{13}{120}t=1 \\ t=\frac{120}{13} \\ t=9.23076923077... \\ t\approx9.23 \end{gathered}[/tex]It will take approximately 9.23 minutes to fill the tank if all pipes are opened together.
When the three pipes are opened, the fraction that has been filled(let's call it as x) is given by:
[tex]\begin{gathered} (\frac{1}{30}+\frac{1}{20}+\frac{1}{40})\cdot3=x \\ x=\frac{13}{40} \end{gathered}[/tex]Then, the slowest pipe(the third pipe) is closed, then, after 3 more minutes we're going to fill an extra y amount of water, given by:
[tex]\begin{gathered} (\frac{1}{30}+\frac{1}{20})\cdot3=y \\ \frac{1}{10}+\frac{3}{20}=y \\ \frac{5}{20}=y \\ y=\frac{1}{4} \end{gathered}[/tex]Then, after a time t with the first pipe open, we're going to fill the tank(remember that it has been filled already by the amounts x and y, therefore, we must subtract it from the total volume).
[tex]\begin{gathered} \frac{1}{30}\cdot t=1-\frac{13}{40}-\frac{1}{4} \\ \frac{t}{30}=\frac{27}{40}-\frac{10}{40} \\ t=30\cdot\frac{17}{40} \\ t=12.75 \end{gathered}[/tex]If the slowest pipe is shut off after 3 minutes and the fastest pipe is shut off 3 minutes later, it will take 12.75 minutes for the remaining open pipe to finish filling the tank.
Can I get help with my math homework I’m struggling with ? 3
Answers
Step 1:
The slope intercept form formula is
y = mx + c
m = slope
c = intercept on the y-axis
Final answer
Slope Intercept
Step
Ton graph the function, find both x=intercept and y-intercept
[tex]\begin{gathered} \text{From y = }\frac{3}{2}x\text{ + 1} \\ y-\text{intercept c = 1} \\ \text{Make x subject of the formula} \\ 3x\text{ = 2y - 2} \\ x\text{ = }\frac{2}{3}y\text{ - }\frac{2}{3} \\ x-\text{intercept c = -}\frac{2}{3} \end{gathered}[/tex]Next plot the graph.
IF AB = (2x + 23). BC = (12 + 7x), and CD = 19 - 9x), find AD.
Answers
The addition of length of each line segment gives the value of AD.
[tex]\begin{gathered} \text{From the number line, AB+BC+CD=AD} \\ AD=(2x+23)+(12+7x)+(19-9x)=2x+7x-9x+23+12+19=54 \end{gathered}[/tex]The value of AD is 54.
Help me solve for equation 6x+3=33
Answers
Given:
[tex]6x+3=33[/tex]is given.
Required:
We need to solve this equation.
Explanation:
Here an equation given as
[tex]6x+3=33[/tex]now add both side negative 3 and we get
[tex]\begin{gathered} 6x+3-3=33-3 \\ 6x=30 \end{gathered}[/tex]now multiply both side with inverse 6
[tex]\begin{gathered} \frac{1}{6}*6x=30*\frac{1}{6} \\ x=5 \end{gathered}[/tex]Final answer:
Solution of given equation is
[tex]x=5[/tex]
20 4/5 whats the decimal number
Answers
20 4/5
it means 20 integers and 4/5
4/5 = 0.8
so the number 20 4/5 is equal to 20.8
answer: 20.8
20 7/8 is 20 integers and 7/8
7/8 = 0.875
so 20 7/8 is equal to 20.875
Please help me with the question and explain your work! 16 through 19 thank you please please please help
Answers
We have the following:
A.
First we find the slope of the line with the following points:
(0, 3) and (5,0)
[tex]m=\frac{0-3}{5-0}=-\frac{3}{5}[/tex]now, for b, with the point (0,3)
[tex]\begin{gathered} 3=-\frac{3}{5}\cdot0+b \\ b=3 \end{gathered}[/tex]The equation is:
[tex]y=-\frac{3}{5}x+3[/tex]B.
The area is:
[tex]\begin{gathered} A=\frac{AC\cdot CB}{2} \\ A=\frac{3\cdot5}{2}=\frac{15}{2} \\ A=7.5 \end{gathered}[/tex]The area is 7.5 square units
for, perimeter:
[tex]\begin{gathered} p=AC+CB+AB \\ AB^2=AC^2+CB^2 \\ AB^2=3^2+5^2=9+25=34 \\ AB=\sqrt[]{34} \\ p=3+5+\sqrt[]{34} \\ p=13.83 \end{gathered}[/tex]The perimeter is 13.83 units
C.
when two lines are perpendicular they fulfill the following
[tex]m_1\cdot m_2=-1[/tex]therefore,
[tex]\begin{gathered} -\frac{3}{5}\cdot m_2=-1 \\ m_2=\frac{5}{3} \end{gathered}[/tex]Therefore, the equation is:
[tex]y=\frac{5}{3}x+3[/tex]can two rays be put together to form a line
Answers
ANSWER:
Only in the case that the rays are opposite.
STEP-BY-STEP EXPLANATION:
We have that a ray is part of a line that has an end point and continues infinitely in a single direction.
Therefore, a pair of opposite rays are two rays that have the same end point and extend in opposite directions. So together a pair of opposing rays always form a straight line.
Graphically a ray and a line are like this:
Answer: if the rays are opposite they will always form a straight line but if the are not opposite they will not form a line
Step-by-step explanation:
QThe image of point A (3, 4) under translation Tis A' (-1,6). What is the translation rule? worth 50 points guy's can someone please give me an answer really quick please!!!
Answers
Here, we want to find the translation rule
Combo 1Combo 2Combo 33 glazed5 glazed4 glazed4 cream filled6 cream filled4 cream filled5 chocolate1 chocolate4 chocolate$38$32$36a)Write a system to represent this situation. Use g for glazed donuts, f for cream filled donuts, and c for chocolate donuts.b)Solve the system ALGEBRAICALLY to find the price of each donuts.
Answers
We will use the following variables :
g for glazed
f for cream filled donuts
c for chocolate donuts
So, the equation for combo 1
3 g + 4 f + 5 c = $38
The equation for combo 2:
5 g + 6 f + c = $32
The equation for combo 3:
4 g + 4 f + 4 c = $36
So, the system of equations are:
3 g + 4 f + 5 c = 38 (1)
5 g + 6 f + c = 32 (2)
4 g + 4 f + 4 c = 36 (3)
B) Now, we need to solve the system of equations:
From equation 3:
4 g + 4 f + 4c = 36
divide all terms by 4
So, g + f + c = 9
Solve for c:
c = 9 - g - f
Substitute with the value of c at the equations (1)
At (1):
3 g + 4 f + 5 (9 - g - f) = 38
3g + 4f + 45 - 5g - 5f = 38
-2g - f = 38 - 45
-2g - f = -7
Multiply all terms by -1
2g + f = 7
Solve for f
f = 7 - 2g
Substitute with f at the equation of c
c = 9 - g - (7 - 2g)
c = 9 - g - 7 + 2g
c = g + 2
So, we have reached to :
f = 7 - 2g and c = g + 2
substitute with f and c at the equation (2)
5g + 6f + c = 32
5g + 6 (7 - 2g) + g + 2 = 32
solve for g
5g + 42 - 12 g + g + 2 = 32
5g - 12g + g = 32 - 42 - 2
-6g = -12
Divide both sides by -2
g = -12/-6 = 2
f = 7 - 2g = 7 - 2 * 2 = 7 - 4 = 3
c = g + 2 = 2 + 2 = 4
So, the cost of glazed = $2
The cost of cream filled = $3
The cost of chocolate = $4
what are the coordinates of the library A (3,4)b. (4,3)c..(2,1)d.(1,2
Answers
To determine the coordinates of the library, for the x-coordinate, you have to draw a vertical line from the library to the x-axis and read where it intersects the x-axis. And to determine the y-coordinate you have to draw a horizontal line from the position of the library towards the y-axis, and read where the line intersects the y-axis:
The x-coordinate is 4 and the y-coordinate is 3, so the coordinates of the library are (4,3)
please help me ASAP!!!
Answers
what decimals are between 0.82 and 0.83
Answers
Answer:
0.82 and 0.83
It is known that the lengths of trout (centimetres) in dams in North America is Normally distributed with a standard deviation of 5 cm. For monitoring purposes, a sample of 15 trout were captured, measured and released. The sample gave a mean of 50 cm and a standard deviation of 2 cm.The 99% confidence interval for the population average length of trout isSelect one:a.(49.3 ; 50.2)b.(49.2 ; 50.9)c.(46.7 ; 53.3)d.(47.8 ; 52.3)e.(46.2 ; 53.8)
Answers
The average length of the trout in the area with a 99% confidence interval is between 46.7 cm and 53.3 cm.
The distribution used should be t distribution as the sample standard deviation is to be used.
We need to build the 99% confidence interval for the population mean . The following information is provided:
Sample Mean = 50
Sample Standard Deviation = 2 cm
Sample Size = 15
The confidence interval for the trout population is computed as shown below:
[tex]\Pr \left({\bar {X}}-{\frac {cS}{\sqrt {n}}}\leq \mu \leq {\bar {X}}+{\frac {cS}{\sqrt {n}}}\right)=0.99\,[/tex]
now we will substitute the values in the equation of the CI.
[tex]{\bar {X}}-{\frac {2.7}{\sqrt {15}}}\leq \mu \leq {\bar {X}}+{\frac {2.7}{\sqrt {15}}}=0.99\,[/tex]
now solving for the confidence interval we get : 47.8 ; 52.3
Lower limit = 50 - 3.307 = 46.69 ≈ 46.7
upper limit = 50 + 3.307 = 53.307 ≈ 53.3
Hence the average length of the trout in the area is between 46.7 cm and 53.3 cm.
To learn more about confidence interval visit:
https://brainly.com/question/24131141
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In the diagram below, quadrilateral ABCD is inscribed in circle P.What is m< DCB?
Answers
ANSWER
A) 70º
EXPLANATION
In quadrilaterals inscribed in a circle, opposite angles are supplementary - their measures add up 180º. Therefore:
[tex]\begin{gathered} m\angle DAB+m\angle DCB=180º \\ 110º+m\angle DCB=180º \\ m\angle DCB=180º-110º \\ m\angle DCB=70º \end{gathered}[/tex]5+3(-2x+1)=16 I need help
Answers
Given:
5 + 3(-2x + 1) = 16
Let's solve for x.
• Step 1:
Use distributive property to expand the parenthesis
5 + 3(-2x) + 3(1) = 16
5 - 6x + 3 = 16
• Step 2:
Combine like terms
-6x + 3 + 5 = 16
-6x + 8 = 16
• Step 3:
Subtract 8 from both sides
-6x + 8 - 8 = 16 - 8
-6x = 8
• Step 4:
Divide both sides by -6
[tex]\begin{gathered} \frac{-6x}{-6}=\frac{8}{-6} \\ \\ x=-\frac{4}{3} \end{gathered}[/tex]ANSWER:
[tex]-\frac{4}{3}[/tex]•
Find each value if f(x) = 2x - 1 and g(x) = 2 - x2.9. f(0)
Answers
ANSWER
f(0) = -1
EXPLANATION
We just have to replace x by 0 into f(x):
[tex]\begin{gathered} f(x)=2x-1 \\ f(0)=2\cdot0-1 \\ f(0)=0-1 \\ f(0)=-1 \end{gathered}[/tex]Find the volume of the sphere. Round your answer to the nearest tenth. Use 3.14 for n. A sphere has a radius of 8 centimeters. The volume of the sphere is about cm?.
Answers
Find the volume of the sphere. Round your answer to the nearest tenth. Use 3.14 for n. A sphere has a radius of 8 centimeters. The volume of the sphere is about cm?.
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\cdot\pi\cdot r^3[/tex]we have
r=8 cm
pi=3.14
substitute the given values in the formula
[tex]\begin{gathered} V=\frac{4}{3}\cdot3.14\cdot8^3 \\ V=2,143.6\text{ cm\textasciicircum{}3} \end{gathered}[/tex]answer is
2,143.6 cubic centimetersA sofa regularly sells for $600. The sale price is $504.00. Find the percent decrease of the sale price from the regular price
Answers
STEP - BY - STEP EXPLANATION
What to find?
Percentage decreaase.
Given:
Original price = $600
new price = $504
Step 1
Recall the formula for percentage decrease.
[tex]\text{ \% decrease=}\frac{decrease}{original\text{ price}}\times100\text{ \%}[/tex]Step 2
Determine the value for the dcerease.
[tex]Decrease=new\text{ price - original price}[/tex][tex]Decrease=504-600=-96[/tex]Step 3
Substitute into the formula and simplify.
[tex]\text{ \% decrease=-}\frac{96}{600}\times100\text{ \%}[/tex][tex]=-16\text{ \%}[/tex]ANSWER
Percent decrease = 16% decrease
1. Drag the fractions in order from least to greatest value L
Answers
Given the fractions 3/4 and 5/16
In order to determine which is less or greater, we need to first express them in percentage as shown;
3/4 = 3/4*100%
3/4 = 3*25 = 75%
5/16 = 5/16 * 100
5/16 = 500/16 = 31.25%
Since 75% is greater than 31.25% hence;
3/4 is greater than 5/16 and the sign that will be in the box will be the greater than sign i.e 3/4>5/16
Strategy: I compared the fraction to the bench mark of >
Suppose Piper eats out twice a week 15% of the time, she eats out once a week 35% of the time, and she does not eat out any time during the week 50% of the time.What is the expected value for the number of times Piper eats out during the week? Round your answer to the nearest hundredth if needed.
Answers
Solution
We are given
Probability of eating out twice in a week = 15% = 0.15
Probability of eating out once in a week = 35% = 0.35
Probability of not eating out in a week = 50% = 0.50
Let X be a random variable of the number of times Piper eats out in a week
So we have the table
Note: The Formula For finding the Expected value E(X) is given by
[tex]E(X)=\sum ^{}_{}xp(x)[/tex]Substituting we get
[tex]\begin{gathered} E(X)=0(0.50)+1(0.35)+2(0.15) \\ E(X)=0+0.35+0.30 \\ E(X)=0.65 \end{gathered}[/tex]Therefore, the expected value is
[tex]E(X)=0.65[/tex]Given sinx= 5/13 andπ/2 < x < π find the exact value of tan 2x
Answers
Given sin(x)=5/13
First, lets find cos(x).
It is known that:
[tex]\begin{gathered} \sin ^2(x)+\cos ^2(x)=1 \\ (\frac{5}{13})^2+\cos ^2(x)=1 \\ \cos ^2(x)=1-\frac{25}{169} \\ \cos ^2(x)=\frac{169-25}{169}=\frac{144}{169} \\ \cos (x)=\pm\sqrt[]{\frac{144}{169}}\text{ = }\frac{\sqrt[]{144}}{\sqrt[]{169}} \\ \cos (x)=\pm\frac{12}{13} \end{gathered}[/tex]Since π/2 < x < π, we are in 2nd quadrant. Then, cos(x) is negative.
[tex]\cos (x)=-\frac{12}{13}[/tex]Since we know the values for sin and cos, we can find tan(x):
[tex]\begin{gathered} \tan (x)=\frac{\sin(x)}{\cos(x)} \\ \tan (x)=\frac{\frac{5}{13}}{-\frac{12}{13}} \\ \tan (x)==-\frac{5}{12} \end{gathered}[/tex]Now, lets work with the expression tan(2x)
It is known that:
[tex]\tan (2x)=\frac{2\tan(x)}{1-\tan^2(x)}[/tex]
Since we know tan(x), we can substitute in the expression above and find the value of tan(2x):
[tex]\begin{gathered} \tan (2x)=\frac{2\tan(x)}{1-\tan^2(x)} \\ \tan (2x)=\frac{2\cdot(-\frac{5}{12}_{})}{1-(-\frac{5}{12})^2} \\ \tan (2x)=\frac{-\frac{10}{12}}{1-\frac{25}{144}}=\frac{-\frac{10}{12}}{\frac{144-25}{144}}=\frac{-\frac{10}{12}}{\frac{119}{144}}=-\frac{10}{12}\cdot\frac{144}{119} \\ \tan (2x)=-\frac{120}{119} \end{gathered}[/tex]Answer: -120/119
A pizza place offers ten different toppings. A special is a pizza with any three different toppings. How many different types of specials are offered?
Answers
As given by the question
There are given that the total of 10 different topping
Now,
According to the question:
There is also talk about 3 different pizzas.
So,
The three different toppings from the 10 different toppings:
[tex]10C_3=\frac{10!}{3!(10-3)!}[/tex]Then,
[tex]\begin{gathered} 10C_3=\frac{10!}{3!(10-3)!} \\ 10C_3=\frac{10!}{3!(7)!} \\ 10C_3=\frac{10\times9\times8\times7!}{3!(7)!} \\ 10C_3=\frac{10\times9\times8}{3\times2\times1} \end{gathered}[/tex]Then,
[tex]\begin{gathered} 10C_3=\frac{10\times9\times8}{3\times2\times1} \\ 10C_3=10\times3\times4 \\ 10C_3=120 \end{gathered}[/tex]Hence, 120 different pizzas are possible.
Fill in only the blanks. (Whatever that has an answer like the domain don’t do it)only do the empty blanks
Answers
From the graph, we can conclude:
[tex]Range\colon(-\infty,1)[/tex]As:
[tex]\begin{gathered} x\to0,f(x)\to-\infty \\ x\to\infty,f(x)\to1 \end{gathered}[/tex]x-intercept:
[tex](1,0)[/tex]Asymptote:
Vertical asymptote:
[tex]x=0[/tex]Horizontal asymptote:
[tex]y=1[/tex]Find the area of the rectangle if the length is y + 4 inches and the width is y - 5 inches. Enter your answer as a polynomial in terms of variable y and in standard form, ay2 + by + c.
Answers
We have the following:
We have that the area of a rectangle is the following
[tex]\begin{gathered} A=l\cdot w \\ \text{In this case:} \\ l=y+4 \\ w=y-5 \end{gathered}[/tex]replacing:
[tex]\begin{gathered} A=(y+4)(y-5)=y^2-5y+4y-20 \\ A=y^2-y-20 \end{gathered}[/tex]find an equation of the line having the given slope and containing the given point . Slope -2; through (6,-9) . type answer in slope-intercept form .
Answers
Given:
The slope of the line is m = -2.
The line passes throught the point (6,-9).
The objective is to find the equation of line.
Explanation:
Consider the point as,
[tex](x_1,y_1)=(6,-9)[/tex]The general equation to find the equation of line in slope intercept form is,
[tex]y-y_1=m(x-x_1)[/tex]Substitution:
On plugging the given values in the general equation,
[tex]\begin{gathered} y-(-9)=-2(x-6) \\ y+9=-2x+12 \\ y=-2x+12-9 \\ y=-2x+3 \end{gathered}[/tex]Here, slope of the line is -2 and y- intercept is 3.
Hence, the equation of the line in slope intercept form is y = -2x + 3.
Help me with this math problem plsWrite the formula for g(x) in terms of f(x)
Answers
Given:
Given a graph of f(x) and g(x).
Required:
To write the formula for g(x) in terms of f(x).
Explanation:
The graph of g(x) is 5 units left and 1 units up gfrom the graph of f(x).
Therefore the function g(x) is
[tex]g(x)=f(x+5)+1[/tex]Final Answer:
[tex]g(x)=f(x+5)+1[/tex]define the imaginary unit, i
Answers
An imaginary unit, i is a solution to the quadratic equation:
[tex]\text{ x}^2\text{ + 1 = 0}[/tex]Or to simply say,
[tex]i\text{ = }\sqrt[]{-1}[/tex]It can
Solve the following system of linear equations by graphing:4x + 4y = 2010x + 2y = 18
Answers
one solution: (1, 4)
The equations:
y = -x + 5
y = -5x + 9
Explanation:[tex]\begin{gathered} \text{Given equations:} \\ 4x+4y=20\text{ }\ldots(1) \\ 10x+2y=18\text{ }\ldots(2) \end{gathered}[/tex]To plot the graphs, we can assign values to x. The we get the corresponding values of y for each of the equation.
Rewritting the two equations by making y the subject of formula:
[tex]\begin{gathered} 4x+4y=20 \\ \text{divide through by 4:} \\ x\text{ + y = 5} \\ y\text{ = -x + 5} \end{gathered}[/tex][tex]\begin{gathered} 10x+2y=18 \\ \text{divide through by 2:} \\ 5x\text{ + y = 9} \\ y\text{ = -5x + 9} \end{gathered}[/tex]Plotting the graphs:
The point of intersection of the graphs is the solution.
There is one solution: (1, 4)