Answer
Equation of the line in slope-intercept form is
y = -3x - 7
Explanation
Two lines that are parallel to each other have the same slopes.
So, we just need the slope of the line 9x + 3y = 8, and the point given for the line we need to write the equation of that line.
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
To find the slope of the line, we need to put the equation given in the form of y = mx + b
9x + 3y = 8
3y = -9x + 8
Divide through by 3
(3y/3) = (-9x/3) + (8/3)
y = -3x + (8/3)
Comparing this with y = mx + b, we can see that
m = slope = -3
So for our line,
The general form of the equation in point-slope form is
y - y₁ = m (x - x₁)
where
y = y-coordinate of a point on the line.
y₁ = This refers to the y-coordinate of a given point on the line
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
x₁ = x-coordinate of the given point on the line
m = slope = -3
Point = (x₁, y₁) = (-1, -4)
x₁ = -1
y₁ = -4
y - y₁ = m (x - x₁)
y - (-4) = -3 (x - (-1))
y + 4 = -3 (x + 1)
y + 4 = -3x - 3
y = -3x - 3 - 4
y = -3x - 7
Hope this Helps!!!
I need to know the answer to this edmentum question.
Solution
[tex]x^{\frac{9}{7}}=x^{1+\frac{2}{7}}=x^1\times x^{\frac{2}{7}}[/tex]Solving on;
[tex]Since\text{ }x^{\frac{a}{b}}=\sqrt[b]{x^a}[/tex]Then,
[tex]x^{\frac{9}{7}}=x\times\sqrt[7]{x^2}=x\sqrt[7]{x^2}[/tex]Solve for x: 3(x-7)= 15
Given
[tex]3(x-7)=15[/tex]To solve for x.
Explanation:
It is given that,
[tex]3(x-7)=15[/tex]Then,
[tex]\begin{gathered} x-7=\frac{15}{3} \\ x-7=5 \\ x=5+7 \\ x=12 \end{gathered}[/tex]Hence, the value of x is 12.
Hi I need help to find the value of Q
Given the system of equations:
x - 3y = 4
2x - 6y = Q
Let's find the value of Q.
Let's solve the equations simulateneously using substitution method.
Rewrite the first equation for x:
• Add 3y to both sides of equation 1
x - 3y + 3y = 4 + 3y
x = 4 + 3y
• Substitute (4 + 3y) for x in equation 2:
2x - 6y = Q
2(4 + 3y) - 6y = Q
• Apply distributive property:
2(4) + 2(3y) - 6y = Q
8 + 6y - 6y = Q
8 + 0 = Q
8 = Q
Q = 8
Therefore, the value of Q is 8
ANSWER:
8
In this diagram, circle A has radius = 4.9 and DC = 8.1. BC is tangent line, calculate the distance of BC.
We have a tangent line that means the m
we have
AB= radius=4.9
AC=AD+DC=4.9+8.1=13
Because we have that m
[tex]c^2=a^2+b^2[/tex]where
a=AB=4.9
b=?=x
c=AC=13
we substitute the values
[tex]\begin{gathered} b=\sqrt[]{13^2-4.9^2} \\ b=\sqrt[]{169-24.01} \\ b=\sqrt[]{144.99} \\ b=12.04 \end{gathered}[/tex]Refer to the figure below to answer the following questions: (a) What is the value of "x"? (b) Angle 4 Given ml 72 1\6x + 23 is equal to how many degrees? _ 4x - 34 5. 6
we get that
[tex]\begin{gathered} 4x-3+6x+23=90\rightarrow \\ 10x+20=90 \\ 10x=70 \\ x=\frac{70}{10}=7 \end{gathered}[/tex]so we have x=7
the angle 4 is equal to
[tex]m\angle4=90-(4\cdot7-3)=90-25=65^{\circ}[/tex]A survey was given to 120 sixth-grade students at a middle school. It showed that 48 students said they like playing at the park. What percent of the students surveyed said they like playing at the park? A 40% B 45% C 60% D 65%
In this case, we'll have to carry out several steps to find the solution.
Step 01:
total students = 120
playing at park students = 48
% = ?
Step 02:
% = part / whole * 100
% = 48 / 120 * 100
% = 40%
The answer is:
40%
The table shows the amounts of onions and tomatoes in batches of different sizes in a sauce recipe.Elena observes that if she takes the number in the column for tomatoes and divides it by the corresponding number in the column for onions, she always gets the same result.What is the meaning of the number that Elena calculated?onions (ounces)246tomatoes (ounces)163248
The meaning of the number that Elena calculated is a ratio.
A ratio says how much of one thing there is compared to another thing.
Sketch the graph of the line whose equation , in point-slope form , is y-3 =9/5 (×+1 ). Also write the equation of this line in slope-intercept form . (y=mx+b)
To sketch this line equation, it would be a good idea to write the equation of the line in the slope-intercept form first.
Finding the equation of the line in slope-intercept formThe equation of the line in the slope-intercept form is given by:
[tex]y=mx+b[/tex]Where:
• m is the slope of the line.
,• b is the y-intercept of the line (the point where the line passes through the y-axis. At this point, x = 0.
Now, we have that the line equation is given in point-slope form as follows:
[tex]y-3=\frac{9}{5}(x+1)[/tex]We can multiply both sides of the equation by 5:
[tex]\begin{gathered} 5(y-3)=5\cdot\frac{9}{5}(x+1) \\ 5(y-3)=\frac{5}{5}\cdot9(x+1)\Rightarrow\frac{a}{a}=1,\frac{5}{5}=1 \\ 5(y-3)=9(x+1) \end{gathered}[/tex]Now, we have to apply the distributive property to both sides of the equation:
[tex]\begin{gathered} 5(y-3)=9(x+1) \\ 5y-15=9x+9 \end{gathered}[/tex]Add 15 to both sides of the equation, and then divide by 5:
[tex]\begin{gathered} 5y-15+15=9x+9+15 \\ 5y=9x+24 \\ \frac{5y}{5}=\frac{1}{5}(9x+24) \\ y=\frac{9}{5}x+\frac{24}{5} \end{gathered}[/tex]Therefore, the equation is slope-intercept form is:
[tex]y=\frac{9}{5}x+\frac{24}{5}[/tex]Sketching the graph for the lineSince we have that the original equation of the line was:
[tex]y-3=\frac{9}{5}(x+1)[/tex]We already know that one of the points of the line is (-1, 3) since the point-slope form of the line is given by:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(3)=\frac{9}{5}(x-(-1)) \\ y-3=\frac{9}{5}(x+1) \end{gathered}[/tex]We need another point to graph the line. We can use the y-intercept obtained before:
[tex]\frac{24}{5}=4.8[/tex]And since we know it is the y-intercept, we have that this point is (0, 4.8). Therefore, we can graph this equation using the following points:
(0, 4.8) and (-1, 3). Then we can sketch the line as follows:
To have a more precise graph for the line, we can use a graphing calculator:
We can see that the line passes through the x-axis at the point:
[tex]\begin{gathered} y=0\Rightarrow y=\frac{9}{5}x+\frac{24}{5} \\ 0=\frac{9}{5}x+\frac{24}{5} \\ -\frac{24}{5}=\frac{9}{5}x \\ \frac{5}{9}\cdot(-\frac{24}{5})=\frac{5}{9}\cdot(\frac{9}{5})x \\ -\frac{24}{9}=x \\ x=-\frac{8}{3}\approx-2.66666666667 \end{gathered}[/tex]The revenue function R in terms of the number of units sold, a, is given as R= 380x - 0.1x^2where R is the total revenue in dollars. Find the number of units sold a that produces a maximum revenue?Your answer is x= What is the maximum revenue? __
The maximum revenue corresponds to the y-coordinate of the vertex of the graph of the revenue function. And the number of units sold that produces a maximum revenue corresponds to the x-coordinate of the vertex of the graph of the revenue function.
Then, we can find the vertex of the revenue function. For this, we can rewrite the function in its vertex form by completing the square.
[tex]\begin{gathered} f(x)=ax^{^2}+bx+c\Rightarrow\text{ General form} \\ f(x)=a(x-h)^2+k\Rightarrow\text{ Vertex form} \\ \text{ Where }(h,k)\text{ is the vertex} \end{gathered}[/tex]Then, we have:
Step 1: Reorder the terms.
[tex]\begin{gathered} R=380x-0.1x^2 \\ R=-0.1x^2+380x \end{gathered}[/tex]Step 2: We use the general form to find the values of a,b and c.
[tex]\begin{gathered} a=-0.1 \\ b=380 \\ c=0 \end{gathered}[/tex]Step 3: We find the value of h using the below formula.
[tex]h=\frac{-b}{2a}[/tex][tex]\begin{gathered} h=\frac{-380}{2(-0.1)} \\ h=\frac{-380}{-0.2} \\ h=1900 \end{gathered}[/tex]Step 4: We find the value of k using the below formula.
[tex]k=c-\frac{b^2}{4a}[/tex][tex]\begin{gathered} k=0-\frac{380^2}{4(-0.1)} \\ k=\frac{-144400}{-0.4} \\ k=361000 \end{gathered}[/tex]Step 5: We substitute the values of a, h and k into the vertex form.
[tex]\begin{gathered} \begin{equation*} f(x)=a(x-h)^2+k \end{equation*} \\ R=-0.1(x-1900)^2+361000 \end{gathered}[/tex]Thus, the vertex of the revenue function is the ordered pair (1900,361000).
AnswerThe number of units sold that produces a maximum revenue is 1900, and the maximum revenue is $361000.
A bicyclist rides 11.2 kilometerseast and then 5.3 kilometers southWhat is the angle of thebicyclist's resultant vector?
Given
A = 11.2 km East
B = 5.3 km south
Find
Angle of the resultant vector
Explanation
Angle of the resultant vector is given by
[tex]tan\emptyset=\frac{Bsin\alpha}{A+Bcos\alpha}[/tex]Here angle between both the vectors is 90 degree
[tex]\begin{gathered} tan\emptyset=\frac{Bsin\alpha}{A+Bcos\alpha}=\frac{11.2(sin90)}{5.3+11.2(cos90)} \\ tan\emptyset=\frac{11.2}{5.3} \\ tan\emptyset=2.11320755 \\ \emptyset=64.67degrees \end{gathered}[/tex]So Angle made from origin = 270+64.67
= 334.67 degree = 334.7 degree(approx)
Final Answer
Angle of resultant Vector = 334.7 degree
Arbuckle County has an area of 1,424 square miles with a population of 854,786 people.a) Determine the population density. Round to the nearest tenth.b.) What is the population density in people per square kilometers (Recall 1 km = 0.62 miles). Round to the nearest tenth.______people per sqaure kilo c.) Baxter County has an area of 2,608 square miles. How many people would be in Baxter County, if the population density were the same as Arbuckle County? Round to the nearest person._____people.
Given that Arbuckle County has an area of:
[tex]1,424\text{ }square\text{ }miles[/tex]And has a population of:
[tex]854,786\text{ }people[/tex]a) You need to use the formula for calculating the Population Density:
[tex]Population\text{ }Density=\frac{Number\text{ }of\text{ }people}{Land\text{ }area}[/tex]Therefore, by substituting values into the formula and evaluating, you get:
[tex]Population\text{ }Density=\frac{854786\text{ }people}{1424\text{ }square\text{ }miles}[/tex][tex]Population\text{ }Density\approx600.3\frac{people}{square\text{ }mile}[/tex]b) You need to convert the area from square miles to square kilometers.
You know that:
[tex]1\text{ }km=0.62\text{ }mi[/tex][tex](1\text{ }km)^2=(0.62\text{ }mi)^2\Rightarrow1km^2=0.3844\text{ }mi^2[/tex]Now you can set up the conversion:
[tex](1424\text{ }mi^2)(\frac{1\text{ }km^2}{0.3844mi^2})[/tex]Evaluating, you get:
[tex]\approx3704.5\text{ }km^2[/tex]Using the formula for Population Density, you get:
[tex]Population\text{ }Density=\frac{854786\text{ }people}{3704.5\text{ }square\text{ }kilometers}[/tex][tex]Population\text{ }Density\approx230.7\frac{people}{square\text{ }kilometer}[/tex]c) You know that Baxter County has an area of 2,608 square miles, if the population density were the same as Arbuckle County, you can substitute values into the formula used before and solve for the number of people:
[tex]600.3=\frac{People}{2608}[/tex][tex]\begin{gathered} 600.3\cdot2608=People \\ People\approx1,565,580 \end{gathered}[/tex]Hence, the answers are:
a)
[tex]600.3\text{ }people\text{ }per\text{ }square\text{ }mile[/tex]b)
[tex]230.7\text{ }people\text{ }per\text{ }square\text{ }kilometer[/tex]c)
[tex]1,565,580\text{ }people[/tex]The graph represents two linear relations. What is the point of intersection of the two lines?
Solution
The graph below shows the point of intersection
Thus, the point of intersection is (20, 32)
Option C
Consider the expressions 3x(x - 2) + 2 and 2x2 + 3x – 16.
For x = 3, each expression has a value of 11. For x = 6, each expression has a value of 74. These results suggest that the expressions are equivalent
Explanation:The given expressions are:
3x(x - 2) + 2 and 2x² + 3x - 16
Substitute x = 3 into 3x(x - 2) + 2
3(3)(3 - 2) + 2
= 9(1) + 2
= 9 + 2
= 11
Substitute x = 3 into 2x² + 3x - 16
2(3)² + 3(3) - 16
2(9) + 9 - 16
18 + 9 - 16
= 11
Substitute x = 6 into 3x(x - 2) + 2
3(6)(6 - 2) + 2
18(4) + 2= 74
Substitute x = 6 into 2x² + 3x - 16
2(6)² + 3(6) - 16
2(36) + 18 - 16
72 + 2
= 74
For x = 3, each expression has a value of 11. For x = 6, each expression has a value of 74. These results suggest that the expressions are equivalent
[tex]7.5 + 5f + 16.2 + 2f[/tex]simplified expression
given :
7.5 + 5f + 16.2 + 2f =
combine like terms
So,
(7.5 + 16.2) + ( 5f + 2f ) = 23.7 + 7f
So,
the simplified expression = 23.7 + 7f
state the direction of opening for f(x)=-(1)/(2)x^(2)+3
The given expression is a quadratic function. If the leading coefficient is greater than zero in a quadratic function, the parabola opens upward, and if the leading coefficient is less than zero, the parabola opens downward. Graphically,
In this case, the leading coefficient is less than zero, the direction of opening is downward.
Where does the line y = 6x - 13 cross the Y axis?
A function cross the y-axis when the value of x is 0.
[tex]y=6x-13[/tex]Find the value of y, when x is 0:
[tex]\begin{gathered} y=6(0)-13 \\ y=-13 \end{gathered}[/tex]Then, the line y=6x-13 crosses the y-axis at y= -13Which set of ordered pairs does not describe a function? Select one : (- 1, 1), (0, 0), (0, 1), (1, 1), (1, 2); (1, 3) , (2, 6) , (3, 9), (4, 12), (5, 15); (- 1, 1), (0, 0), (1, 1), (2, 4), (3, 9); (1, 2), (2, 3), (3, 4), (4, 5) , (5, 6) It’s five in each row btw
To be able to determine which set of pairs does not describe a function, that set of pairs mustn't have a complete set of totally unique pairs which a function should have.
Let's check.
1.) (- 1, 1), (0, 0), (0, 1), (1, 1), (1, 2)
- This set of pairs don't have a unique set of pairs. This does not describe a function.
2.) (1, 3) , (2, 6) , (3, 9), (4, 12), (5, 15)
- This set of pair have a unique set of pairs. This does describe a function.
3.) (- 1, 1), (0, 0), (1, 1), (2, 4), (3, 9)
- Not all of its sets of pairs are unique. This does not describe a function.
4.) 1, 2), (2, 3), (3, 4), (4, 5) , (5, 6)
- This set of pair have a unique set of pairs. This does describe a function.
Therefore, the answer is 1 and 3.
find the area and the circumference of a circle with a diameter of 6 yards use the value 3.14 for it and do not round your answer be sure to include the correct unit in your answer
Given a circle with a diameter of 6 yards
The radius of the circle (r) = half of the diameter (d)
so,
[tex]r=0.5\cdot d=0.5\cdot6=3\text{ yards}[/tex]The area of the circle is given by the formula:
[tex]\text{Area}=\pi\cdot r^2[/tex]Use: pi = 3.14
so,
[tex]\text{Area}=3.14\cdot3^2=3.14\cdot9=28.26\text{ square yards}[/tex]The circumference is given using the formula:
[tex]C=2\cdot\pi\cdot r[/tex]So, the circumference is:
[tex]C=2\cdot3.14\cdot3=18.84\text{ yards}[/tex]so, the answer is:
Area = 28.26 square yards
Circumference = 18.84 yards
The times, in seconds, for 8 athletes who ran a 100 m sprint on the sametrack are shown below. Find the mean time (seconds).10.2, 10.8, 10.9, 10.3, 10.2, 10.4, 10.1, and 10.4
Given: Time records for 8 athletes who ran 100 m sprint is 10.2, 10.8, 10.9, 10.3, 10.2, 10.4, 10.1, and 10.4 (in seconds).
Required: To determine the mean time.
Explanation: The mean of n number of observations is the ratio of the sum of all the observations to the number of observations.
Thus,
[tex]Mean=\frac{10.2+10.8+10.9+10.3+10.2+10.4+10.1+10.4}{8}[/tex]Further solving-
[tex]\begin{gathered} Mean=\frac{83.3}{8} \\ =10.4125 \end{gathered}[/tex]Final Answer: The mean time is 10.4125 seconds.
x = y +10x = 2y + 3(17,7)is it consistent and independent
Simplify the equation to obtain the y coordinate.
[tex]\begin{gathered} y+10=2y+3 \\ 2y-y=10-3 \\ y=7 \end{gathered}[/tex]Substitute 7 for y in the equaation x = y +10 to obtain the value of x.
[tex]\begin{gathered} x=7+10 \\ =17 \end{gathered}[/tex]So solution of equations is (17,7).
The equations consist of the solution, so equation is consistent and equation has only one solution those equation is independent.
Thus it is consistent and independent.
Find the radius of the circle containing 60° arc of a circle whose length is 14 m.
Given:
It is given that
[tex]\begin{gathered} \theta\text{ = 60}^0 \\ Arc\text{ length = 14}\pi \end{gathered}[/tex]Required:
The radius of the circle
Explanation:
The length of an arc is given by the formula,
[tex]\begin{gathered} Arc\text{ length = }\frac{\theta}{360}\text{ }\times\text{ 2}\pi r \\ \end{gathered}[/tex]Substituting the values in the formula,
[tex]\begin{gathered} 14\pi\text{ = }\frac{60}{360}\text{ }\times\text{ 2}\times\pi\times r \\ r\text{ = }\frac{14\times360}{60\times2} \\ r\text{ = }\frac{5040}{120} \\ r\text{ = 42} \end{gathered}[/tex]Answer:
Thus the radius of the circle is 42 m.
if m<10=77, m<7=47 and m<16=139, find the measure of the missing angle m<8=?
Line a and line b are two parallel lines and a cut by the transverse c and d.
But to obtain what angle 8, we will only consider the transverse c.
Below is a plot:
The measure of angle 10 = The measure of angle 8
(Reason: They are alternate angles and alternate angles are equal)
Hello, can you please help me solve question 3 !!
Use the next trigonometric rules:
[tex]\begin{gathered} \cos 2t=\cos ^2t-\sin ^2t \\ \\ \sin ^2t=1-\cos ^2t \end{gathered}[/tex]Use Cos2t
[tex]\cos ^2t-\sin ^2t-2\sin ^2t=0[/tex]Combine similar terms:
[tex]\cos ^2t-3\sin ^2t=0[/tex]Use sin²t:
[tex]\begin{gathered} \cos ^2t-3(1-\cos ^2t)=0 \\ \\ \cos ^2t-3+3\cos ^2t=0 \end{gathered}[/tex]Combine similar terms:
[tex]4\cos ^2t-3=0[/tex]Add 3 in both sides of the equation:
[tex]\begin{gathered} 4\cos ^2t-3+3=0+3 \\ 4\cos ^2t=3 \end{gathered}[/tex]Divide both sides of the equation into 4:
[tex]\begin{gathered} \frac{4\cos ^2t}{4}=\frac{3}{4} \\ \\ \cos ^2t=\frac{3}{4} \end{gathered}[/tex]Find the square root of both sides of the equation:
[tex]\begin{gathered} \sqrt[]{\cos^2t}=\sqrt[]{\frac{3}{4}} \\ \\ \cos t=\pm\frac{\sqrt[]{3}}{2} \\ \\ \cos t=+\frac{\sqrt[]{3}}{2} \\ \\ \cos t=-\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]Use the unit circle to find wich angles in the given interval have a cos equal to:
[tex]\cos t=\pm\frac{\sqrt[]{3}}{2}[/tex]Solution:
[tex]t=\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}[/tex]Without doing any calculations, compare expression A to expression B.5A.x 2506B. (250) + ({ x 250)ХChoose the words to complete the comparison.Expression A is Choose...v expression B.r
We have two expressions and we have to compare them.
We don't need to calculate the exact value of each expression. We can left them as products of 250.
Then, expression A is already 5/6 of 250.
We can rearrange expression B as:
[tex]\begin{gathered} B=(\frac{1}{3}\cdot250)+(\frac{1}{2}\cdot250) \\ B=(\frac{1}{3}+\frac{1}{2})\cdot250 \\ B=\frac{2+3}{3\cdot2}\cdot250 \\ B=\frac{5}{6}\cdot250 \end{gathered}[/tex]Expression B is also 5/6 of 250, so the two expressions are equal.
Answer: expression A is equal to expression B.
Select the correct answer. Consider these functions: $($)=3.13 + 2 g(t)=V Which statements, if any, are true about these functions? 1. The function fg(x)) = x for all real x. II. The function & x)) = x for all real x. III. Functions fand gare inverse functions. O A. I only B. ll only C.I, II, and III D. None of the statements are true.
Let's verify every statement:
I.
[tex]f(g(x))=3(\sqrt[3]{\frac{x-2}{3}})^3+2=3(\frac{x-2}{3})+2=x-2+2=x[/tex]So, the first one is true.
II:
[tex]g(f(x))=\sqrt[3]{\frac{(3x^3+2)-2}{3}}=\sqrt[3]{x^3}=x[/tex]So, this one is true
III.
Since:
[tex](fog)(x)=(gof)(x)=x[/tex]We can conclude that f(x) and g(x) are inverse functions. So, this statements is also true
Answer:
C.I, II, and III
5 Which of the following functions are an example of continuous growth?
In order to have a function that represents continuous growth, the base value that has a variable as exponent must be the constant value "e":
[tex]\begin{gathered} f(x)=a\cdot b^{cx}\\ \\ b=e \end{gathered}[/tex]Looking at the options, the functions that have this base value are options I and II.
Therefore the correct option is A.
How do I solve this problem? I need to graph the segment
Step 1:
Draw a table of time with inches of snow.
One of every four doctors recommended Tylenol. If there are 2250 doctors, approximately how many recommended the medicine ?PLEASE HELP OMG I NEED TO TURN IN THIS QUESTION SOON AS POSSIBLE PLEASE. A.225B.560C.850D.10,000
1 out of 4 doctors recommended the medicine.
That means, one-fourth, of the total doctors recommended the medicine.
We know the total number, 2250.
We take one-fourth of it.
Shown below:
[tex]\frac{1}{4}\times2250=\frac{2250}{4}=562.5[/tex]Matching to answer choices, we see that B is correct.
Convert 205° to radians. Radians = degrees timesPie/180
The number in degree is 205º
The expression to convert degree into radians is by multiply the given angle degree by π/180.
[tex]\begin{gathered} \text{Radians}=\frac{180}{\Pi}\times205 \\ \text{Radians }=3.578 \end{gathered}[/tex]205º is written as 3.578 radians
Choose the operation you need to perform first. 2. 3+5x8+2 (1 point) O add 3 and 5 multiply 5 and 8 together Odivide 8 by 2
2)
The order of operations is shown below
P = parentheses
E = exponent
M = multiplication
D = division
A = addition
S = subtraction
The given expression is 3 + 5 x 8 ÷ 2
The first sign in the expression when we follow the order of operations above is multiplication(x). Thus, the correct option is
multiply 5 and 8 together