Answers
Okay, here we have this:
Considering the provided function, we obtain that:
As have the form: y=mx+b, it's a line.
Now, let's find the x- and y-intercepts:
x-intercept:
0=((1)/(2)) x+((3)/(5))
-3/5=1/2x
x=-3/5*2
x=-6/5
Here we obtain that the x-intercept is (-6/5, 0)
y-intercept:
y=1/2x+3/5
y=1/2(0)+3/5
y=3/5
Here we obtain that the y-intercept is (0, 3/5)
Finally we obtain that the graph is:
Related Questions
Prove the following statements by contraposition (or directly if you prefer or are able to)
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ANSWER
[tex]Preposition:\text{ if }\frac{1}{r}\text{ is irrational, then }r\text{ is irrational}[/tex][tex]proof:\text{ suppose }\frac{1}{r}=\frac{1}{\sqrt{p}}[/tex]where square root of 'p' is not a perfect square
[tex]Thus:\text{ }r=\sqrt{p}[/tex][tex]\text{ Therefore}:r\text{ is irrational}[/tex]Drag the black dots to move the like terms next to each other. Then simplify the expression. 5x^2+3x-8+x^2-2x+4
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The question is given to be:
[tex]5x^2+3x-8+x^2-2x+4[/tex]The common terms are shown below:
[tex]\begin{gathered} x^2\Rightarrow5x^2,x^2 \\ x\Rightarrow3x,-2x \\ Cons\tan t\Rightarrow-8,4 \end{gathered}[/tex]Therefore, the arranged expression will be:
[tex]\Rightarrow5x^2+x^2+3x-2x-8+4[/tex]The simplified expression will then become:
[tex]\Rightarrow6x^2+x-4[/tex]Evaluate the following expression when 8x-7 when x=7
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They ask for the evaluated expression:
[tex]8x-7[/tex]When x=7
So, actually, we will answer a number and not an expression. Now, to find this number we're going to replace all the places that appear x in the original expression, with the given value of x.
Then, we have:
[tex]8(7)-7[/tex][tex]56-7[/tex][tex]49[/tex]So, we can conclude that the correct answer is 49.
Now draw a line through the yellow center that is perpendicular to the linethat you just drew.111Y-10-9-87-6-5433 4 5 678 9 10-10
Answers
Firstly we need to find the equation of the line drawn
The slope intercept form of the line equation is;
[tex]y=mx+b[/tex]where;
m = slope
b = intercept (y axis)
From the graph, we can see that the y intercept is
What is the slope of the line graphed below?(3,3)5(0-6)What is m=
Answers
In the diagram, we give the coordinates as follows
(0,-6) where 0 is x(1) and -6 is y(1)
Also,(3,3) where 3 is x(2) and 3 is y(2)
The slope of a line (m) can be solved with the formula below:
[tex]\begin{gathered} \text{slope(m)}=\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]We then insert the coordinates into the formula
[tex]\begin{gathered} m=\frac{3-(-6)}{3-0} \\ m=\frac{3+6}{3} \\ m=\frac{9}{3} \\ m=3 \end{gathered}[/tex]Therefore the slope of the line is 3.
Note: m and the slope are the same.
Solve each system by substitution. y=3x+4 y=4x+7
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We need to solve the following system by substituition:
[tex]\begin{cases}y=3x+4 \\ y=4x+7\end{cases}[/tex]To solve by substituition means that we need to isolate one variable in one of the equations and replace one expression with the other. This is done below:
[tex]\begin{gathered} (3x+4)=4x+7 \\ 3x+4=4x+7 \\ 3x-4x=7-4 \\ -x=3 \\ x=-3 \end{gathered}[/tex]Then we need to replace the value of "x" in any of the two equations.
[tex]\begin{gathered} y=3\cdot(-3)+4 \\ y=-9+4 \\ y=-5 \end{gathered}[/tex]The solution is (-3,-5).
need help What are the intervals that it's increasing, decreasing, and constant?What is the range of the function?Is the function odd and even?
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The domain of a function is the set of values of x for which the function is true.
To determine the domain of the function, you have to identify the values of x that correspond to the function.
The function starts at x= -3 and ends at x= 3, so the domain of the function is all values of x between -3 and 3.
Written using interval notation, the domain of the function is:
[tex]{}[-3,3][/tex]This function can be divided into four parts.
The first part goes from x=-3 to x=-1, within this interval the function has a negative slope, which means that for the interval [-3,-1] the function decreases.
The second part of the function goes from x=-1 to x= 0, within this interval [-1,0] the function has a positive slope, which means that the function increases.
The third part of the function goes from x=0 to x=1, within this interval [0,1] the function has a negative slope, so the function decreases.
The fourth part of the function goes from x=1 to x=3, within this interval [1,3] the function has a positive slope, which means that the function increases.
Range
The range of the function is the set of values of y for which the function is true.
This function takes a value between y=0 and y=1, so the range of the function expressed in interval notation is:
[tex][0,1][/tex]
A function is even when it is symmetrical with respect to the y-axis, and it can be considered to be odd when it is symmetrical about the x-axis.
If there is symmetry about the y-axis, then both parts of the function will look like a reflection.
In this case, the function is symmetrical about the y-axis, so you can conclude that this is an even function.
Price of Plums8What is the slope ofthe line?76[?]Price ($)32Give your answer asa fraction in simplestform.11 2 3 4 5 6 7 8 9Number of Plums
Answers
SOLUTION
The slope of a line is define as a changes in x with a coreeepounding changes in y
Hence
[tex]\text{Slope}=\frac{\text{change in y}}{change\text{ in x}}=\frac{\Delta y}{\Delta x}[/tex]Slope is given by the formula
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]From the graph given in the image, we have the following points
[tex]\begin{gathered} (0,0) \\ \text{and } \\ (4,1) \end{gathered}[/tex]Where
[tex]\begin{gathered} x_1=0,x_2=4 \\ y_1=0,y_2=1_{} \end{gathered}[/tex]su
5. What number is 0.25% of 46?
Answers
We need to find which number is 0.25% of 46
[tex]0.25\%=\frac{0.25}{100}=\frac{25}{100000}[/tex]So, the number will be :
[tex]0.25\%\cdot46=\frac{25}{10000}\cdot46=0.115[/tex]So, the answer is : 0.115
One group (A) contains 105 people. Three-fifths of the people in group A will be selected to win $15 fuel cards. There is another group (B) in a nearby town that will receive the same number of fuel cards, but there are 122 people in that group. What will be the ratio of nonwinners in group B after the selections are made? Express your ratio as a fraction or with a colon.
Answers
Okay, here we have this:
First we will find the number of winners of group A:
# of Winners (A)=105(3/5)=315/5=63
This mean that the number of winner in group A and B is 63 people.
Now, according with this let's find the proportion of non-winners in group B:
Number of nonwinners group B=122-63=59
The ratio of nonwinner=59/122
It says Graph a Right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form.(4,4) and (-4,2) I've shown the photo and it wants me to find Leg 1, Leg 2 and the hypotenuse I've already made an attempt to solve it and it was wrong.
Answers
Answer:
[tex]\begin{gathered} Hypothenuse=2\sqrt[]{17} \\ \text{base}=8 \\ \text{height}=2 \end{gathered}[/tex]Step by step explanation:
To calculate the hypotenuse of the triangle, we are going to use the distance between points formula. It is represented by the following expression:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Then, with the points (-4,2) and (4,4)
[tex]\begin{gathered} d=\sqrt[]{(4-(-4))^2+(4-2)^2} \\ d=\sqrt[]{8^2+2^2} \\ d=\sqrt[]{64+4} \\ d=\sqrt[]{68} \\ d=2\sqrt[]{17} \end{gathered}[/tex]Then, for the legs:
coordinates for the base (-4, 2) and (4,2)
[tex]\begin{gathered} \text{base}=\sqrt[]{(4-(-4))^2+(2-2)^2} \\ \text{base}=\sqrt[]{64} \\ \text{base}=8 \end{gathered}[/tex]for the height: (4,2) and (4,4)
[tex]\begin{gathered} \text{height}=\sqrt[]{(4-4)^2+(4-2)^2} \\ \text{height}=\sqrt[]{2^2} \\ \text{height}=2 \end{gathered}[/tex]have some free Coins!! by answering this question...
x3+y3+z3=k
and i know the answer so.. if you got it right i will give you a brainiest
Answers
What are we solving for? x, y, z??
Answer: you think of the integers for x, y, and z so that x³+y³+z³=8? Sure. One answer is x = 1, y = -1, and z = 2. But what about the integers for x, y, and z so that x³+y³+z³=42
Step-by-step explanation:
im not sure about this answer, but i tried
You are making a triangle-shaped pennant out of fabric. The base of the pennant is 5 inches and the height is 13 inches. How many fabric do you need to make the pennant?
Answers
Explanation
the area of a triangle is given by:
[tex]\text{Area}=\frac{base\cdot heigth}{2}[/tex]the, to know the fabric you need, you need to finde the area
Let
base=5 in
heigth=13 inches
now, replace.
[tex]\begin{gathered} \text{Area}=\frac{base\cdot heigth}{2} \\ \text{Area}=\frac{5\text{ in}\cdot13\text{ in}}{2} \\ \text{Area}=\frac{65in^2}{2} \\ \text{Area}=32.5in^2 \end{gathered}[/tex]I hope this helps you
solve the system of equations by substitution. check your answer 6x-9=yy=-3x
Answers
substitute x = 1 into y = -3x
[tex]\begin{gathered} y=-3(1_{}) \\ y=-3 \end{gathered}[/tex]Hence, x = 1. y= -3
The number of people aged 18 to 24 years old who smoked decreased according to the CDC. In 2005, 24.7% of the age group smoked, and that number declined to 19.3% in 2010.Assume the rate of change is linear keep a running difference and round each smoker to the nearest tenth
Answers
If each year the percentage changes the same amount and we have six years from 2005 to 2010:
1. 2005
2. 2006
3. 2007
4. 2008
5. 2009
6. 2010
If we want to know that difference between years, then we have to divide the total change in five parts:
[tex]\begin{gathered} 24.7-19.3=5.4 \\ \frac{5.4}{5}=1.08 \end{gathered}[/tex]Then it changes 1.08% each year. So if we substract that quantity each year from 2005, at 2010we should have 19.3%:
1. 2005: 24.7%
2. 2006: 24.70% - 1.08% = 23.62%
3. 2007: 23.62% - 1.08% = 22.54%
4. 2008: 22.54% - 1.08% = 21.46%
5. 2009: 21.46% - 1.08%= 20.38%
6. 2010: 20.38% - 1.08% = 19.3%
Now we round each to the nearest tenth:
1. 2005: 24.7%
2. 2006: 23.62% ≅ 23.6%
3. 2007: 22.54% ≅ 22.5%
4. 2008: 21.46% ≅ 21.5%
5. 2009: 20.38% ≅ 20.4%
6. 2010: 19.3%
4. Which expression is equivalent to 7-7-5? (4 points)O 72077FIN
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The expression is 7³ * 7⁻⁵
To solve this you have to apply the law of exponents
[tex]a^b\cdot a^c=a^{(b+c)}[/tex]So for the expression it is
[tex]7^3\cdot7^{(-5)}=7^{(3-5)}=7^{-2}[/tex]The negative exponent "-2" means that the value is inverted following the law:
[tex]\times^{-1}=\frac{1}{x}[/tex][tex]7^{-2}=\text{ }\frac{1}{7^2}[/tex]Answer 7⁻²= 1/7²
1. If the temperature at 3:00 in the afternoon is 31.5°C and become 35°C, what is the average temperature? What is asked? A. temperature B. the average temperature C. 35°C, 31.5°C D. multiplication, addition
Answers
Answer
B. The average temperature, which is 33.25 °C
Step-by-step explanation
The average between two values is computed as follows:
[tex]average=\frac{value\text{ 1 + value 2}}{2}[/tex]In this case, we need to calculate the average between 31.5 °C and 35 °C, then:
[tex]\begin{gathered} average\text{ temperature = }\frac{31.5+35}{2} \\ average\text{ temperature=}\frac{\text{66.5}}{\text{2}} \\ average\text{ temperature=33.25 \degree C} \end{gathered}[/tex]hello how are you I am under da waterpls help me, here too much raining *blub*
Answers
Answer
The value of the $500 invested at 2.5% after 20 years = $819.31
Explanation
The amount that an initial amount, A₀, becomes at a compound interest of r% over a period of time, t, is given as
A = A₀ (1 + r)ᵗ
where
A = Value of the money saved over a period of time t
A₀ = Initial value of the money saved = $500
r = Rate = 2.5% yearly = 0.025
t = Time = 20 years
A = A₀ (1 + r)ᵗ
A = 500 (1 + 0.025)²⁰
A = 500 (1.025)²⁰
A = 500 (1.6386)
A = $819.31
Hope this Helps!!!
Graphing a line by first finding its x- and y-intercepts
Answers
Okay, here we have this:
We need to graph the following equation by first finding its x- and y-intercepts:
x-intercept:
[tex]\begin{gathered} -\frac{2}{3}x+3=0 \\ -\frac{2}{3}x=-3 \\ -2x=-9 \\ x=\frac{9}{2}=4.5 \end{gathered}[/tex]Here we obtain that the x-intercept is (4.5, 0).
y-intercept:
[tex]\begin{gathered} y=-\frac{2}{3}\cdot\: 0+3 \\ y=-0+3 \\ y=3 \end{gathered}[/tex]
Here we obtain that the y-intercept is (0, 3).
Now, let's graph this:
Angela uses point (4, 3) to represent the location of her house and uses the point (10, 8) to represent the location of a gas station. Each unit on the graph represents 1 miles. She wants to drive to the gas station using a straight line. How far is the gas station from Angela's house?
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ANSWER
7.8 miles
EXPLANATION
We have that Angela's house is at point (4, 3) and the gas station is located at (10, 8).
We want to find the straight line distance (in miles) between her house and the gas station.
To do that, we need to find the distance between the two points on the graph.
Since each unit is 1 mile, we then convert the distance (in units) to miles.
The distance between two coordinate points on a graph is given as:
[tex]D\text{ = }\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]where (x1, y1) and (x2, y2) are the two points.
So, we have that:
[tex]\begin{gathered} D\text{ = }\sqrt[]{(10-4)^2+(8-3)^2}=\sqrt[]{6^2+5^2} \\ D\text{ = }\sqrt[]{36\text{ + 25}}\text{ = }\sqrt[]{61} \\ D\text{ = 7.8 units} \end{gathered}[/tex]Therefore, converting to miles:
1 unit = 1 mile
=> 7.8 units = 7.8 miles
Therefore, the gas station is 7.8 miles far from Angela's house.
You choose one card from a standard deck. What is the probability of selecting a Ace OR a Red card?Please write your anwer as a reduced fraction.
Answers
A standard deck has 52 cards
there are 26 red cards and 26 black cards
there are 4 aces in the deck
so the probability for an ace is 4/52
the probability of a red card is 26/52= 0.5
now adding both probabilities it gets
0.5 + 1/13
Hello I would like to ask if you could help me with this problem. 8÷2(2+2)=?
Answers
1
Explanation:
8÷2(2+2)
[tex]\begin{gathered} 8\text{ : 2(2+2)} \\ \text{Solve what is in the bracket} \\ 8\colon\text{ 2(4)} \\ 8\colon\text{ 8} \\ \text{ratio here means division} \\ \frac{8}{8}\text{ = 1} \end{gathered}[/tex]Therefore, 8÷2(2+2)= 1
Let g(x) be the transformation of f(x) = IxI such that the vertex is at (2, 5). Identify the rule for g(x) and its graph.
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First remember that we have the initial function f(x)=|x| and we make 2 movements to the function in order to obtain g(x), lets's see what are those movements:
As you can see if we subtract -2 from the inside of the absolute value we move graph 2 positions to the right, now lets sum 5 to the function and see what happens
If we sum 5 to the function from outside the absolute value we move the graph 5 units up.
Se the answer to the question is the first option.
What is the slope of a line that is perpendicular to the line whose equation is 2x+7y=5?A. 7/2B. 2/7C. −7/2D. −7/5
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We have the followed expression for a giving line:
[tex]2x+7y=5[/tex]Isolating the Y we find the expression:
[tex]y=\frac{-2}{7}x\text{ + }\frac{5}{7}[/tex]We know that if a line with expression y=mx+b is perpendicular to the line that the question gave to us, the product of the slopes of the two lines must be:
[tex]\frac{-2}{7}\times m=-1[/tex]With this last expression, we can find the slope for the line perpendicular to our first line:
[tex]\frac{-2}{7}\times m=-1\text{ }\Rightarrow\text{ m=}\frac{7}{2}[/tex]So, our slope is 7/2
In a recent year, the total scores for a certain standardized test were normally distributed, with a mean of 500 and a standard deviation of 10.3. Answer parts (a)-(d) below.(a) Find the probability that a randomly selected medical student who took the test had a total score that was less than 487.The probability that a randomly selected medical student who took the test had a total score that was less than 487 is(Round to four decimal places as needed.)(b) Find the probability that a randomly selected medical student who took the test had a total score that was between 499 and 512.The probability that a randomly selected medical student who took the test had a total score that was between 499 and 512 is(Round to four decimal places as needed.)(c) Find the probability that a randomly selected medical student who took the test had a total score that was more than 527.The probability that a randomly selected medical student who took the test had a total score that was more than 527 is(Round to four decimal places as needed.)(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.
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First, we will find the z-score associated with a score of 487
(x – μ) / σ = (500-487)/10.3 =13/10.3 = 1.26213
Then P = 0.8962 according to the z-table
which is the answer to a part
(-5, -3); slope = -3/5writing linear equations
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To find the equation, we use the point-slope formula.
[tex]y-y_1=m(x-x_1)[/tex]Where,
[tex]\begin{gathered} m=-\frac{3}{5} \\ x_1=-5 \\ y_1=-3 \end{gathered}[/tex]Let's replace them.
[tex]\begin{gathered} y-(-3)=-\frac{3}{5}(x-(-5)) \\ y+3=-\frac{3}{5}x-3 \\ y=-\frac{3}{5}x-3-3 \\ y=-\frac{3}{5}x-6 \end{gathered}[/tex]Therefore, the equation is[tex]y=-\frac{3}{5}x-6[/tex]a side of the triangle below has been extended to form an exterior angle of 131 degrees. find the value of x
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The sum of the angles (x and the one that measures 131°), is 180 degrees, they are suplementary angles
[tex]\begin{gathered} x+131=180 \\ x=180-131 \\ x=49 \end{gathered}[/tex]x is 49°
equation match a.) m= -2/3, b=3b.) m = -3/2, (4,-1)
Answers
Given:
A.)
Slope of the line (m) = -2/3
Y-intercept (b) = 3
The given can be used to make an equation under the Slope-Intercept Form:
[tex]\text{ y = mx + b}[/tex]By substituting m and b to y = mx + b, we can generate the equation.
We get,
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (-2/3)x + (3)}[/tex][tex]\text{ y = -}\frac{2}{3}x\text{ + 3}[/tex][tex]3(\text{ y = -}\frac{2}{3}x\text{ + 3)}[/tex][tex]3y\text{ = -2x + 9}[/tex][tex]2x\text{ + 3y = 9}[/tex]Therefore, the equation match to m = -2/3 and b = 3 is 2x + 3y = 9.
B.)
Slope of the line (m) = -3/2
x,y = 4,-1
To be able to generate the equation, let's first determine the y-intercept (b). We can get it by substituting m = -3/2 and x,y = 4,-1 to the equation y = mx + b.
We get,
[tex]\text{ y = mx + b}[/tex][tex]\text{ -1= (-3/2)(4) + b}[/tex][tex]-1\text{ = }\frac{-12}{2}\text{ + b }\rightarrow\text{ -1 = -6 + b}[/tex][tex]\text{ b = -1 + 6}[/tex][tex]\text{ b = 5}[/tex]Since we now found that the y-intercept (b) = 5, let's substitute b and m = -3/2 to y = mx + b to generate the equation.
We get,
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (-3/2)x + (5)}[/tex][tex]\text{ y = -}\frac{3}{2}x\text{ + 5}[/tex][tex]\text{ -2(y = -}\frac{3}{2}x\text{ + 5)}[/tex][tex]\text{ -2y = 3x - 10}[/tex]Therefore, the equation that match m = -3/2 and (4,-1) is -2y = 3x - 10.
Write this ratio as a fraction in simplest form without any units. 54 ounces to 3 pounds You can use the table below to help convert the units. Length Weight Capacity (Volume) 1 foot = 12 inches 1 yard = 3 feet 1 pound 16 ounces 1 pint = 2 cups 1 quart 2 pints 1 gallon = 4 quarts = =
Answers
Given:
54 ounces to 3 pounds and units table.
Required:
Write this ratio as a fraction in simplest form without any units.
Explanation:
To solve this, we have relation
[tex]1pound=16ounces[/tex]Now,
[tex]\begin{gathered} =\frac{54ounces}{3pounds} \\ =\frac{54ounces}{3\times16ounces} \\ =\frac{54ounces}{48ounces} \\ =\frac{9}{8} \end{gathered}[/tex]Answer:
[tex]\text{ The answer is }9:8.[/tex]
I will show you a pic
Answers
The solution of the given lines are the point at which the intersecting lines meet
In the given graph :
the lines are meet at the point ( -3, - 8)
x = -3, y = - 8
Answer : C) The solution of the given equation of line is (x,y) = (-3, -8)