Answers
From the graph provided we can determine two points which are;
[tex]\begin{gathered} (x_1,y_1)=(0,-3) \\ (x_2,y_2)=(2,0) \end{gathered}[/tex]For the equation of the line given in slope-intercept form which is;
[tex]y=mx+b[/tex]We would begin by calculating the slope which is;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We can now substitute the values shown above and we'll have;
[tex]\begin{gathered} m=\frac{(0-\lbrack-3\rbrack)}{2-0} \\ m=\frac{0+3}{2} \\ m=\frac{3}{2} \end{gathered}[/tex]Now we have the slope of the line as 3/2, we can substitute this into the equation and we'll have;
[tex]\begin{gathered} y=mx+b \\ \text{Where;} \\ x=0,y=-3,m=\frac{3}{2} \end{gathered}[/tex]We now have the equation as;
[tex]\begin{gathered} -3=\frac{3}{2}(0)+b \\ -3=0+b \\ b=-3 \end{gathered}[/tex]We now have the y-intercept as -3. The equation now is;
[tex]\begin{gathered} \text{Substitute m and b into the equation,} \\ y=mx+b \\ y=\frac{3}{2}x-3 \end{gathered}[/tex]The graph of this is now shown below;
We shall now draw lines to indicate the 'rise' and 'run' of this graph.
ANSWER
Observe carefully that the "Rise" is the movement along the y-axis (3 units), while the "Run" is the movement along the x-axis (2 units).
This clearly defines the slope of the equation that is;
[tex]\frac{\Delta y}{\Delta x}=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{3}{2}[/tex]
Related Questions
Construct a pair of parallel lines with a set of alternate interior angles that measure X degrees.X=60 degrees
Answers
Given:
An angle is x= 60 degrees.
Required:
Construct a pair of parallel lines with a set of alternate interior angles that measure X degrees.
Explanation:
First, draw a line then construct an angle of 60 degrees.
Now take a point B on the line that is making an angle of 60 degrees cut the arc from point B with the same measure of arc A.
Now cut the arcs from point A that join the line l and from C that joins m as with the same arc. Draw a line with the intersecting arc.
Thus the angle
[tex]\theta[/tex]will be an interior angle of measures 60 degrees.
Final Answer:
The figure is attached in the explanation part.
If the vertices of three squares are connected to form a right triangle, the sum of the areas of the two smaller squares is the same as the area of the largest square. Based on this statement and the model below, what is the area of square B? (Figure is not drawn to scale.) B 8 m 2 289 m
Answers
One square has area 289 square meters, and the other has area
[tex]8m\times8m=64m^2[/tex]Then, since the sum of the two areas of the smaller squares is equal to the area of the big square, we have
[tex]\begin{gathered} B+64m^2=289m^2 \\ B=289m^2-64m^2 \\ B=225m^2 \end{gathered}[/tex]Solve the system of equations by adding or subtracting.S3x + y = 412x + y = 0The solution of the system is
Answers
Step 1:
Choose either Substitution or elimination method to solve system of equation.
Step 2:
If you choose substitution,
firstly, name the equation
3x + y = 4 .............................1
2x + y = 0 ..............................2
secondly, choose one of the equation and make one of the varable subject of the relation
2x + y = 0 .......................1
y = -2x
Step3
substitute y in equation 2
3x + (-2x) = 4
3x - 2x = 4
x = 4
Step 4:
find y from y = -2x
y = -2(4)
y = -8
( 4 ), ( -8 )
Answer:
x = 4
y = - 8
Step-by-step explanation:
3x + y = 4
2x + y = 0
(3x + y ) (-1 ) = 4 ( - 1 )
2x + y = 0
- ( 3x + y ) = - 4
2x + y = 0
Question 9 (1 point) Jennifer is a car saleswoman. She is paid a salary of $2200 per month plus $300 for each car that she sells. Write a linear function that describes the relationship between the number of cars sold x and the monthly salary y. Then, graph the function to show the relationship.
Answers
How do I understand Standard Form of a Line? I don't know how to do it.
Answers
There are several forms in which one can write the equation of a line. Have in mind that TWO variables should be included in the equation. These two variables are: x and y.
If you type the equation in a form that looks like:
A x + B y = C
where the A, B, and C are actual numbers (like for example: 3 x - 2 y = 5)
This is the standard form of a line. to recognize it notice that bith variables x an y appear in separate terms on the LEFT of the equal sign., and a pure number (no variables) appears on the right of the equal sign.
Another form of writing the equation of a line is in the so called "solpe-intercept" form. This form looks like:
y = m x + b
Notice that in this case the variable ÿ" appears isolated on the left , and on the right of the equal sign you get a term with the variable x, and another constant (pure number) term (b). Like for example in the case of:
y = 3 x
A couple of friends decide to race each other. Emmet can run 6 yards per second, whereas Ayana can run 9 yards per second. Because he is slower, Emmet also gets a head start of 30 yards. Shortly after they start running, Ayana will catch up to Emmet. How far will Ayana have to run?Write a system of equations, graph them, and type the solution.
Answers
We know the formula d=rt where d is distance, r is rate and t is time
Emmet:
d = 6 yd/s * t
Ayana:
d = 9 yd/s * t
We give Emmet 30 less yards to run
Emmet:
d - 30 = 6 yd/s * t
d = 6t + 30
Setting the equations equal to each other
9 * t = 6t + 30
Subtract 6t from each side
9t-6t = 30
3t = 30
Divide by 3
3t/3 = 30/3
t = 10 seconds
It will take 10 seconds for Ayana to catch up
Ayana:
d = 9 yd/s * t
d = 8 * 10 = 90 yds
Solve the system. Is the answer (3,0) or (0, -1) or no solution or infinitely many solutions?
Answers
Given:
[tex]\begin{gathered} \frac{1}{3}x+y=1\ldots..(1) \\ 2x+6y=6\ldots\text{.}(2) \end{gathered}[/tex]Solve the system of equations.
Equation (2) can be simplified as,
[tex]\begin{gathered} 2x+6y=6 \\ \text{Divide by 6 on both sides} \\ \frac{2x}{6}+\frac{6y}{6}=\frac{6}{6} \\ \frac{1}{3}x+y=1\text{ which represents the equation (1)} \end{gathered}[/tex]Moreover, the slope and y-intercept of both the equation of lines are the same.
It shows that the lines are coincident.
The system has an infinite number of solutions. Also, point (3,0) is one of the solutions.
In the diagram below, BS and ER intersect as show. Determine the measure of
Answers
timmy stated that the product of 3/3 and 12 is greater than the product of 3/2 and 12. is timmy correct?
Answers
Hence the product of 3/3 and 12 is not greater than the product of 3/2 and 12.
So timmy is not correct
3a^2 -3a - 36. solving quadratic by factoring. factor each expression. be sure to check for greatest common factor first.
Answers
we have the expression
[tex]3a^2-3a-36[/tex]step 1
Factor 3
[tex]3(a^2-a-12)[/tex]step 2
equate to zero
[tex]3(a^2-a-12)=0[/tex]step 3
Solve
[tex](a^2-a-12)=0[/tex][tex]\begin{gathered} a^2-a=12 \\ (a^2-a+\frac{1}{4}-\frac{1}{4})=12 \\ (a^2-a+\frac{1}{4})=12+\frac{1}{4} \\ (a^2-a+\frac{1}{4})=\frac{49}{4} \end{gathered}[/tex]Rewrite as perfect squares
[tex](a-\frac{1}{2})^2=\frac{49}{4}[/tex]take the square root on both sides
[tex]\begin{gathered} a-\frac{1}{2}=\pm\frac{7}{2} \\ a=\frac{1}{2}\pm\frac{7}{2} \end{gathered}[/tex]the values of a are
a=4 and a=-3
therefore
[tex]3(a^2-a-12)=3(a-4)(a+3)[/tex]Simplify to create an equivalent expression. 2(3r + 7) - (2 +r) Over Choose 1 answer: Intro INCORRECT (SELECTED 4r + 12 You might have confused terms. Sub B 5r + 13 809 C 5r + 12
Answers
The frist step in simplifying the expression is expanding the term on the left. This gives
[tex]2(3r+7)=6r+14[/tex]therefore, the expression becomes
[tex]2(3r+7)-(2+r)=6r+14-(2+r)[/tex]and since
[tex]-(2+r)=-2-r[/tex]the above becomes
[tex]6r+14-2-r[/tex]Adding/subtracting the like terms gives
[tex]6r-r+14-2[/tex][tex]5r+12[/tex]which is our answer!
Please help solve thank you
Answers
a) 2711/7576
b) 43
=================================================
Explanation:
a) 2711 are e-bikes and there are 3277+2711+1588 = 7576 total bikes. Divide the values to get 2711/7576 . This fraction cannot be reduced because the GCF of 2711 and 7576 is 1.
---------
b) There are 3277 bikes with fat tires out of 7576 total. Use a calculator to get 3277/7576 = 0.43255 approximately. This converts to 43.255% and then rounds to 43%
The percent sign is already typed in, so you just need to type in the whole number 43 for this box.
Find the surface area of the prism. 8 cm. 3 cm. 3 cm. 3 cm.) - 3 cm. Surface Area cm2
Answers
Surface area of a rectangular prism:
[tex]\begin{gathered} SA=2(l\cdot h+w\cdot h+l\cdot w) \\ l=\text{lenght} \\ w=\text{width} \\ h=\text{height} \end{gathered}[/tex]For the given prims:
l=8cm
w=3cm
h=3cm
[tex]\begin{gathered} SA=2(8\operatorname{cm}\cdot3\operatorname{cm}+3\operatorname{cm}\cdot3\operatorname{cm}+8\operatorname{cm}\cdot3\operatorname{cm}) \\ SA=2(24cm^2+9cm^2+24cm^2) \\ SA=2(57cm^2) \\ SA=114cm^2 \end{gathered}[/tex]Then, the surface area is 114 square centimetersFrom question: Montell is practicing his violin. He is able to play six songs for every nine minutes he practices.*Picture has the table and other questions*
Answers
Answer:
The complete table:
6 18 2 42
9 27 3 63
Explanation:
We know that for every 9 minutes Montell practices he is able to play 6 songs. This means that the ratio between the number of minutes practices to the number of songs played is
[tex]\frac{\min}{\text{song}}=\frac{9}{6}[/tex]Therefore, if we want to solve for minutes plated, we just multiply both sides by 'song' to get
[tex]song\times\frac{\min}{\text{song}}=\frac{9}{6}\times\text{song}[/tex]which gives
[tex]min=\frac{9}{6}\times\text{song}[/tex]This means the number of minutes practised is 9/6 of the number of songs played.
Now 9/ 6 can be simplfied by dividing both the numerator and the denominator by 3 to get
[tex]\frac{9\div3}{6\div3}=\frac{3}{2}[/tex]therefore, we have
[tex]min=\frac{3}{2}\times\text{song}[/tex]Now we are ready to fill the table.
If Montell plays 18 songs then we have
[tex]\min =\frac{3}{2}\times18[/tex][tex]\min =27[/tex]the minutes practised is 27 for 18 songs.
If Montell practices for 3 minutes then we have
[tex]3=\frac{3}{2}\times\text{song}[/tex]then the value of song must be song = 2, since
[tex]\begin{gathered} 3=\frac{3}{2}\times2 \\ 3=3 \end{gathered}[/tex]Hence, for 3 minutes of practice, Montell sings 2 songs.
Now for 42 songs, the number of minutes played would be
[tex]\min =\frac{3}{2}\times42[/tex]which simplifies to give
[tex]\min =63[/tex]Hence, for 42 songs played, the practice time is 63 minutes.
To summerise, the complete table would be
songs 6 18 2 42
minutes 9 27 3 63
through: (-5,4) perpendicular to x=5
Answers
First let's calculate the slope of the straight line
For slopes that are perpendicular to each other we can use the following formula
[tex]m1m2=-1[/tex]Where
m1 = original slope
m2 = perpendicular slope
[tex]\begin{gathered} m2=-\frac{1}{m1} \\ m2=-\frac{1}{5} \end{gathered}[/tex]Now for the intersection
[tex]\begin{gathered} b=y-mx \\ b=4-(\frac{-1}{5})\cdot(-5) \\ b=4-1 \\ b=3 \end{gathered}[/tex]The equation of the line that passes through the point (-5,4) with a slope of -1/5 is
[tex]y=-\frac{1}{5}x+3[/tex]what would the annual rate of interest have to be? round to two decimal places.
Answers
To find:
The rate of interest.
Solution:
It is known that the rate of interest is given by:
[tex]r=n[(\frac{A}{P})^{\frac{1}{nt}}-1][/tex]Here. P = 60000, A = 61200, t = 2.5 and n = 12.
[tex]\begin{gathered} r=12[(\frac{61200}{60000})^{\frac{1}{12(2.5)}}-1] \\ r=0.00792366 \end{gathered}[/tex]Change into the percentage by multiplying by 100:
[tex]\begin{gathered} r=0.00792366 \\ r=0.79\% \end{gathered}[/tex]Thus, the answer is 0.79% per year.
A random sample of CGCC students found that 19% say math is their favorite subject with a margin of error of 2.5 percentage points.a) What is the confidence interval? % to %b) What does the confidence interval mean?
Answers
If 19% say that math is their favorite subject, with a margin of error of 2.5%, then the confidence of interval is:
[tex]\begin{gathered} Confidence\text{ of interval= 19\% math }\pm\text{ 2.5\% margin of error} \\ Confidence\text{ of interval= 16.5\% to 21.5\%} \end{gathered}[/tex]b) The confidence of interval is the range of values in which you think the study or the values are going to fall between if anyone redo the study, it doesn't contain the margin of error because this percentage means the probability that the values aren't going to fall between the confidence of interval.
Express your answer as a polynomial in standard form.f(x) = x^2 + 6x +7g(x) = x + 2Find: g(f(x)
Answers
1) Firstly, let's find the composite function g(f(x)) plugging into the x variable in g(x) the function f(x):
[tex]\begin{gathered} g(f(x))=(x^2+6x+7)+2 \\ g(f(x))=x^{2}+6x+9 \end{gathered}[/tex]2) To write that as the standard form, let's replace g(f(x)) with "y" and write the polynomial orderly to the greatest coefficient to the least one.
[tex]y=x^2+6x+9[/tex]How many flowers, spaced every 6 inches, are needed to surround a circular garden with a 50 foot radius? Round to the nearest whole number if needed
Answers
Given:
The radius of the circular garden is 50 feet.
First, find the circumference of the circle.
[tex]\begin{gathered} C=2\pi\times r \\ C=2\pi(50) \\ C=100\times3.14 \\ C=314 \end{gathered}[/tex]As we know that 6 inches equal 1/2 feet.
[tex]\frac{314}{\frac{1}{2}}=314\times2=628[/tex]Answer: There are 628 flowers will be needed for 314 feet circular garden.
What is the probability that a data value in a normal distribution is between a Z score of -1.52 and Z score of -.34
Answers
We are asked to find the probability that a data value in a normal distribution is between a Z score of -1.52 and -0.34
[tex]P(-1.52First, we need to find out the probability corresponding to the given two Z-scoresFrom the Z-table, the probability corresponding to the Z-score -1.52 is 0.0643
From the Z-table, the probability corresponding to the Z-score -0.34 is 0.3669
So, the probability is
[tex]\begin{gathered} P(-1.52Therefore, the probability that a data value in a normal distribution is between a Z score of -1.52 and a Z score of -0.34 is 30.3%Option A is the correct answer.
y = 2x - 4 Find the solution/root/zero.
Answers
The solution of the linear equation y = 2 · x - 4 is x = 2.
How to find the solution of a linear equationLinear equations are first order polynomials. In this problem we need to solve for x in a linear equation, this can be done by means of algebra properties. The complete procedure is shown below.
Step 1 - We find the find the following expression:
y = 2 · x - 4
Step 2 - We make y equal to zero and we use the symmetric property for equalities:
2 · x - 4 = 0
Step 3 - By compatibility with addition, existence of additive inverse, modulative, associative and commutative properties
2 · x = 4
Step 4 - By compatibility with multiplication, existence of multiplicative inverse and modulative, associative and commutative properties we get the following result:
x = 2
The solution of the linear equation is x = 2.
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[tex] \frac{x - 2}{x + 3} + \frac{10x}{x {}^{2 } - 9}[/tex]simplify the sum. state any restrictions on the variables.
Answers
We have
[tex]\frac{x-2}{x+3}+\frac{10x}{x{}^2-9}[/tex]first, we need to factorize the next term
[tex]x^2-9=(x+3)(x-3)[/tex]so we have
[tex]\frac{x-2}{x+3}+\frac{10x}{(x+3)(x-3)}[/tex]Remember in order to sum a fraction the denominator must be the same
[tex]\frac{(x-2)(x-3)+10x}{(x+3)(x-3)}[/tex]then we solve the multiplications (x-2)(x-3)
[tex]\frac{x^2-3x-2x+6+10x}{(x+3)(x-3)}=\frac{x^2+5x+6}{(x+3)(x-3)}[/tex]then we can factorize the numerator
[tex]x^2+5x+6=(x+3)(x+2)[/tex]so the simplification will be
[tex]\frac{x^2+5x+6}{(x+3)(x-3)}=\frac{(x+3)(x+2)}{(x+3)(x-3)}=\frac{(x+2)}{(x-3)}[/tex]the final result is
[tex]\frac{(x+2)}{(x-3)}[/tex]Can you help me please and thank you very much
Answers
Answer:
∠ FAE = 120°
Step-by-step explanation:
4x and 2x are a linear pair and sum to 180° , that is
4x + 2x = 180
6x = 180 ( divide both sides by 6 )
x = 30
then
∠ FAE = 4x = 4 × 30 = 120°
What's the volume of a cube with a side length of 3 inches?
Answers
ANSWER
27 in³
EXPLANATION
The volume of a cube is the cube of its side length, L,
[tex]V=L^3[/tex]So, if a cube has a side length of 3 inches, then its volume is,
[tex]V=3^3in^3=27\text{ }in^3[/tex]Hence, the volume of a cube with a side length of 3 inches is 27 cubic inches.
use the graph to find the following A) find the slope of the lineB) is the line increasing or decreasingC) estimate the vertical intercept(x y)=
Answers
The Solution.
To find the slope of the line from the given graph:
First, we shall pick two coordinates in the graph, that is
[tex](0,2),(2,-1)[/tex]This implies that
[tex]\begin{gathered} (x_1=0,y_1=2)\text{ and} \\ (x_2=2,y_2=-1) \end{gathered}[/tex]By formula, the slope is given as below:
[tex]\text{ slope=}\frac{y_2-y_1}{x_2-x_1}[/tex]substituting the values in the above formula, we get
[tex]\begin{gathered} \text{ Slope=}\frac{-1-2}{2-0} \\ \\ \text{ Slope =}\frac{-3}{2} \end{gathered}[/tex]So, the slope of the line is -3/2
b. From the graph, and from the slope being a negative value, it is clear that the line graph is Decreasing.
c. To estimate the vertical intercept is to find the y-intercept of the line.
Clearly from the graph, we can see that the vertical intercept is (0,2), that is, the point where the line cut the y-axis.
Therefore, the vertical intercept is (0,2).
Which exponential function is represented by the table below? x –2 0 2 4 y 16 4 1 14
Answers
An exponential function which is represented by the table above is: f(x) = 4(1/2)^x
What is an exponential function?An exponential function simply refers to a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function can be modeled by using this equation:
f(x) = abˣ
Where:
a represents the initial value.b represents the rate of change.From the table above, we would calculate the value of a and b:
At x = 0 and y = 4; the value of a (initial value) is 4.
Rate of change, b = Δy/Δx
Rate of change, b = 1/2
Substituting the parameters into the formula, we have;
f(x) = abˣ
f(x) = 4(1/2)^x
Check:
f(x) = 4 × (1/2)^x f(x) = 4 * ( 1/2 )^x
f(x) = 4 × (1/2)² f(x) = 4 × (1/2)⁻²
f(x) = 4 × 1/4 f(x) = 4 × 4
f(x) = 1 f(x) = 16
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What polynomial identity should be used to prove that 40 = 49 − 9?
a
Difference of Cubes
b
Difference of Squares
c
Square of a Binomial
d
Sum of Cubes
Answers
A polynomial identity that should be used to prove that 40 = 49 − 9 is: B. Difference of Squares.
What is a polynomial function?A polynomial function is a mathematical expression which comprises variables (intermediates), constants, and whole number exponents with different numerical value, that are typically combined by using the following mathematical operations:
AdditionMultiplication (product)SubtractionIn Mathematics, the standard form for a difference of two (2) squares is modeled or represented by this mathematical expression:
a² - b² = (a + b)(a - b).
Where:
a and b are numerical values (numbers or numerals).
Given the following equation:
40 = 49 − 9
40 = 7² - 3³
40 = (7 + 3)(7 - 3).
40 = (10)(4)
40 = 40 (proven).
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What is the volume of a hemisphere with a radius of 6.5 in, rounded to the nearesttenth of a cubic inch?
Answers
To calculate the volum of a hemisphere
We use the formula;
V = (2/3)πr³
where r = radius
π is a constant equal 3.14
r= 6.5 in and π = 3.14
Substituting into the formula
V = (2/3) x 3.14 x (6.5)³
Evauluate
V = (2/3) x 3.14 x 274.625
V = (2/3) x 862.3225
V=574.8816666666667
V= 574.89 in³ to the nearest tenth of a cubic inch.
I'm having a problem with this logarithmic equation I will include a photo
Answers
For the vertical asymptotes, we set the argument of the logarithm to be zero. Therefore,
[tex]\begin{gathered} x-8=0 \\ x-8+8=0+8 \\ x=8 \\ \text{Vertical asymptotes: x = 8} \end{gathered}[/tex]The domain of the function can be found below
[tex]\begin{gathered} x-8>0 \\ solve\text{ the inequality to obtain the domain} \\ x>8 \\ solve\text{ for x to obtain the domain: x>8 or interval form :(8, }\infty\text{)} \end{gathered}[/tex]The following are all 5 quiz scores of a student in a statistics course. Each quiz was graded on a 10-point scale.6, 8, 9, 6, 5,Assuming that these scores constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.
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For this type of problem we use the following formula:
[tex]\begin{gathered} \sigma=\sqrt[]{\frac{\sum^{}_{}(x_i-\mu)^2}{N},} \\ \\ \end{gathered}[/tex]where μ is the population mean, xi is each value from the population, and N is the size of the population.
First, we compute the population mean in order to do that we use the following formula:
[tex]\mu=\frac{\Sigma x_i}{N}\text{.}[/tex]Substituting each value of x_i in the above formula we get:
[tex]\mu=\frac{6+8+9+6+5}{5}=\frac{34}{5}=6.8.[/tex]Now, we compute the difference of each x_i with the mean:
[tex]\begin{gathered} 6-6.8=-0.8, \\ 8-6.8=1.2, \\ 9-6.8=2.2, \\ 6-6.8=-0.8, \\ 5-6.8=-1.8. \end{gathered}[/tex]Squaring each result we get:
[tex]\begin{gathered} (-0.8)^2=0.64, \\ (1.2)^2=1.44, \\ (2.2)^2=4.84, \\ (-0.8)^2=0.64, \\ (-1.8)^2=3.24. \end{gathered}[/tex]Now, we add the above results:
[tex]0.64+1.44+4.84+0.64+3.24=10.8.[/tex]Dividing by N=5 we get:
[tex]\frac{10.8}{5}=2.16.[/tex]Finally, taking the square root of 2.16 we obtain the standard deviation,
[tex]\sigma=\sqrt[]{2.16}\approx1.47.[/tex]Answer:
[tex]\sigma=1.47.[/tex]