When Thelma earns a 6% commission based on the negotiated sale price, the amount earned is $9180.
How to calculate the value?From the information, Thelma is a real estate agent negotiating the sale of a property with a listed price of $180,000. The buyer and seller of the property have agreed to a sale price that is 15% lower than the listed price.
The sales price will be:
= $180000 - (15% × $180000)
= $180000 - $27000
= $153000
Sine she earns 6% commission, this will be:
= Percentage × Sale price
= 6% × $153000
= 0.06 × $153000
= $9180
The commission is $9180.
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How many times can 3x go into -14x^2
[tex]-14x^2 \div 3x\implies \cfrac{-14x^2}{3x}\implies -\cfrac{14}{3}\cdot \cfrac{x^2}{x}\implies -\cfrac{14}{3}x[/tex]
Look at this graph What is the equation of the line in point slope form? Use the red point in your equation. Write your answer using integers, proper fractions, and improper fractions in simplest form. y - ____ = ____ (x - ____)
EXPLANATION
Given the line on the graph, we need to find the slope and the y-intercept.
Considering two ordered pairs, as for instance (x₁,y₁)=(50,-90) and (x₂,y₂)=(80,90)
The slope-equation is:
[tex]\text{Slope}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]Replacing terms:
[tex]\text{Slope}=\frac{(90-(-90))}{(80-50)}=\frac{180}{30}=\frac{18}{3}=6[/tex]The point-slope form of the line is:
y-y₁= m(x-x₁)
Finally, we need to represent as a point-slope form considering either one ordered pair, as for instance, (x₁,y₁)=(50,-90)
y-(-90) = 6(x-50) [Simplifying terms]
y + 90 = 6(x-50) [ANSWER]
What is the slope of the line that passes through the points (-2, 2) and (-4, -1)?
Write your answer in simplest form.
The slope of line through points (-2, 2) and (-4, -1) is 3/2 by using the slope-point formula that tells that change in y divided by change in x.
What is slope?A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
What is point?A point is a basic concept in classical Euclidean geometry that represents an exact location in space and has no length, width, or thickness. In contemporary mathematics, a point more broadly refers to a component of a set known as a space.
Here,
The points are (-2, 2) and (-4, -1)
m=(y2-y1)/(x2-x1)
m=Δy/Δx
m=(-1-2)/(-4+2)
m=3/2
By dividing the change in y by the change in x, the slope of the line passing through the points (-2, 2) and (-4, -1) is 3/2.
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Is the ordered pair a solution of the equation?
y = x + 16; (-1,-17)
a. yes
b. no
Answer:
b.
Step-by-step explanation:
No, because -1 is x and -17 is y. if You plug it in, it will look like this:
-17=-1+16
-1+16=15
15 is not equal to -17, so the answer is no, b.
Hope this helps!
Answer:
a.)yes. у=х+16
Answer:
(-1)
Use the figure to find measures of the numbered angles.
The measure of the numbered angles formed by the common transversal to the two parallel lines are;
[tex] \angle 1 = 113^{ \circ} [/tex]
[tex] \angle 2 = 67^{ \circ} [/tex]
[tex] \angle 3 = 67^{ \circ}[/tex]
[tex]\angle 4 = 113^{ \circ} [/tex]
What are the relationships between the angles formed by the common transversal to two parallel lines?The relationships between the angles are;
Corresponding angles are congruentVertical angles are congruentSame side exterior angles are supplementarySame side interior angles are supplementaryAlternate interior angles are congruentAlternate exterior angles are congruentThe given angle is 113°
According to corresponding angles theorem, we have;
[tex] \angle 1 = 113^{ \circ} [/tex]
[tex]\angle 1 \: and \: \angle 4 [/tex] are vertical angles
According to vertical angles theorem, we have;
[tex]\angle 1 = \angle 4 = 113^{ \circ} [/tex]
[tex] \angle 3 \: and \: 113^{ \circ} [/tex] are same side exterior angles.
According to same side exterior angles theorem, we have;
[tex] \angle 3 \: and \: 113^{ \circ} [/tex] are supplementary angles. Which gives;
[tex] \angle 3 + 113^{ \circ} = 180^{ \circ} [/tex]
[tex] \angle 3 = 180^{ \circ} - 113^{ \circ} = 67^{ \circ}[/tex]
[tex] \angle 2 \: and \: \angle 3 [/tex] are vertical angles, which gives;
[tex] \angle 2 = \angle 3 [/tex] = 67°
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A soccer ball is kicked on a field and follows the path of a parabola. It reaches a maximum height of 80 feet above the ground after traveling 160 feet from where it was kicited.a) Draw a diagram to represent this situation.b) Write an exact equation in vertex form to model this situation.c) Suppose there is a 30 feet tree 280 feet from where the ball was kicked. Will the ball sail over the tree? If yes, by how much? If not, by how much?
a) We will draw the situation.
b) Considering the theory, the vertex of a parabola is represented in (h,k) where h is the x-coordinate, in this case, if our parabola has an amplitude of x=320feet then h=320/2=160feet, and k is the highest y-coordinate 80 feet. So the equation is:
[tex]\begin{gathered} y=a(x-h)^2+k \\ y=a(x-160)^2+80 \end{gathered}[/tex]We have to know the value for a, so we will use a point to replace it in the equation and with that, we will know the value, so in x=0 the y-value is 0 too so:
[tex]\begin{gathered} 0=a(0-160)^2+80 \\ a(-160)^2=-80 \\ a=-\frac{80}{25600}=-\frac{1}{320} \end{gathered}[/tex]So the equation is:
[tex]y=-\frac{1}{320}(x-160)^2+80[/tex]c. To know the answer to this question we will have to replace x=280feet with the y value we will know if at the moment the ball can go over the tree or if it would crash into it.
[tex]\begin{gathered} y=-\frac{1}{320}(280-160)^2+80 \\ y=35feet \end{gathered}[/tex]At that point, the ball would be 35 feet up so if it could pass over the tree 5 feet higher.
Can someone pls answer thiss!! rlly need help asap
The inverse of f(x) will be a relation if the original function's graph contains any location where a horizontal line would cross itself twice, but the inverse of that function won't be a function in and of itself.
Does a function's inverse always represent a relationship?
Essentially, obtaining an inverse is only a matter of changing the x and y coordinates. Although it might not always be a function, this newly generated inverse will be a relation. Sometimes a function's inverse isn't actually a function!
The inverse will also be a function if all horizontal lines only ever intersect one place on the original graph.
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Please help.
Answer choices:
ASA
SSS
AAS
HL
Answer:
sss
Step-by-step explanation:
When the internet first launched, it was slow, clogged up phone lines and was most certainly not cheap. In fact, most Internet service providers (ISP) charged a flat rate access fee that included 20 hours a month of internet time. After twenty-hours of use, the ISP’s charged an additional per-hour fee. Suppose in 1995, Charter charged a flat rate of $39.95 for the first twenty hours of service and an additional per-hour charge of $5.99.a. How much would a Charter bill for 18 hours of internet used be in 1995? b. How much would a Charter bill for 28 hours of internet used be in 1995?
from the question, we were told in 1995, Charter charged a flat rate of
$39.95 for the first twenty hours.
and an additional per hour charge of $5.99
if,
for 20 hours = 39.95
therefore for 1 hour = 39.95/20
so for 18 hours = 39.95/20 X 18.95/20
so for 18 hours = 9
so,
to get the amount Charter bill for 18 hours in 1995 is,
39.95 x 18/20
= 39.95 x 0.9
= $35.955
so Charter bill for 18 hours of internet used in 1995 is $35.955
ould bill for 28 hours is
so, what Charter would
1) If a horizontal asymptote exists for this function, identify its location.4x + 6x3x3 - 2x + 1AyoB3B) y =4OyD Does Not Exist
For this problem, we are given the following rational function:
[tex]f(x)=\frac{4x^3+6x}{3x^3-2x+1}[/tex]We need to determine the horizontal asymptote for this function. In order to determine this, we need to calculate the limit of the function when x approaches infinity. We have:
[tex]\lim_{x\rightarrow\infty}\frac{4(\infty)^3+6\cdot\infty}{3(\infty)^3-2\cdot\infty+1}=\frac{4}{3}[/tex]The horizontal asymptote exists at y= 4/3. The correct option is C.
Traci planted a tree in her backyard.She made this graph to show the tree growth over 5 years. 100 POINTS IF YOU HELP!!!!
A. The slope of the function = 1.5.
a = 15; b = 3; c = 3; d = 1.5
B. y-intercept (b) = 7.5
C. The equation of the function is: y = 1.5x + 7.5.
The height in 10 years is approximately 17.5 feet.
How to Write the Equation of a Linear Function?The equation of a function can be expressed as y = mx + b, if we know the value of the slope, m, and the value of the y-intercept, b.
Part A:
Using the two points on the graph, we can find the slope of the function as shown below:
The two points are (3, 12) and (5, 15):
Slope of the function = (15 - 12)/(5 - 3)
= 3/2
Slope (m) = 1.5.
Thus, the values that represents each letters would be:
a = 15; b = 3; c = 3; d = 1.5
Part B: The y-intercept of the function
The y-intercept of the function can be defined as the initial tree height which is the point where the line intercepts the y-axis of the graph.
Substitute m = 1.5 and (x, y) = (3, 12) into y = mx + b to find the y-intercept (b) of the function:
12 = 1.5(3) + b
12 = 4.5 + b
12 - 4.5 = b
7.5 = b
b = 7.5
y-intercept (b) = 7.5
Part C: To write the equation of the function, substitute m = 1.5 and b = 7.5 into y = mx + b:
y = 1.5x + 7.5.
Therefore, the initiate tree height is 7.5 feet, and it increases at a rate of 1.5 feet per year.
To find the height in 10 years, substitute x = 10 into the equation of the function, y = 1.5x + 7.5:
y = 1.5(10) + 7.5
y = 10 + 7.5
y = 17.5 feet
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suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.5 and a mean diameter of 205 inches. if 79 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by less than 0.3 inches? round your answer to four decimal places.
The probability that the mean diameter of the sample shafts would vary from the population mean by less than 0.3 inches exists 0.0757.
How to estimate population mean?Let X the random variable that represent the diameters of interest for this case, and for this case we know the following info
Where [tex]$\mu=205$[/tex] and [tex]$\sigma=1.5$[/tex]
Let the probability be
[tex]$P(205-0.3=204.7 < \bar{X} < 205+0.3=205.3)$$[/tex]
For this case they select a sample of n = 79 > 30, so then we have enough evidence to utilize the central limit theorem and the distribution for the sample mean can be approximated with:
[tex]$\bar{X} \sim N\left(\mu, \frac{\sigma}{\sqrt{n}}\right)$$[/tex]
To simplify this problem is utilizing the normal standard distribution and the z score given by:
[tex]$z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$$[/tex]
To find the z scores for each limit and we got:
[tex]$z=\frac{204.7-205}{\frac{1.5}{\sqrt{79}}}=-1.778$$[/tex]
[tex]$z=\frac{205.3-205}{\frac{1.5}{\sqrt{79}}}=1.778$$[/tex]
To find this probability:
P(-1.778 < Z < 1.778) = P(Z < 1.778) - P(Z < -1.778)
simplifying the above equation, we get
= 0.962 - 0.0377
= 0.9243
The interest exists the probability that the mean diameter of the sample shafts would vary from the population mean by more than 0.3 inches utilizing the complement rule we got:
P = 1 - 0.9243 = 0.0757
The probability that the mean diameter of the sample shafts would vary from the population mean by less than 0.3 inches exists 0.0757.
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I have two cans of paint. Can a has 9 parts of blue paint to one part of yellow paint. Can b is 20 percent blue paint and the rest is yellow paint. How much paint should i use from each can to obtain 9 liters of paint which is half blue and half yellow.
The amount of paint that must be used from can A and can B is 3.86 liters and 5.14 liters respectively to obtain 9 liters of paint which is half blue and half yellow.
Can A has 9 parts of blue paint and 1 part of yellow paint, this can be expressed in percentage as;
Can A = 90% blue, 10% yellow
Similarly,
Can B = 20% blue, 80% yellow
Now consider an algebraic expression as follows;
A + B = 9 liters
90% A + 20% B = 50% [Blue]
10% A + 80% B = 50% [Yellow]
Resolving;
90% A + 20% B = 10% A + 80% B
80% A = 60% B
Solving the equation, A + B = 9, for one variable;
A + B = 9
B = 9 - A
80% A = 60% (9 - A)
80% A = 540% - 60% A
140% A = 540%
A = 3.86 Liters
Now solving for B;
B = 9 - A
B = 9 - 3.85
B = 5.14 Liters
Therefore 3.86 liters should be used from can A and 5.14 liters should be used from can B.
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determine the equation of the line from the graph
Answer:
y = -x + 1
Step-by-step explanation:
y =mx + b
It is crossing the y axis at 1 that is the b
The slope (m) is -1. From one point on the line to another you go down 1 and left 1. That represents a negative slope of 1
5.
Examine the diagram at right. Then use the
information provided in the diagram to find the
measures of angles a, b, c, and d. For each angle,
name the relationship from your Angle
Relationships Toolkit that helped justify your
conclusion. For example, did you use vertical
angles? If not, what type of angle did you use?
Based on angle relationships, the missing angle measures are:
a = 118° [same side exterior angles]
b = 118° [vertical angles]
c = 32° [Linear pair]
d = 32° [same side interior angles]
How to use Angle Relationship to Find to Find Measures of Angles?Some of the angle relationships that can be used to determine the measures of angles that are formed when two parallel lines are intersected by a transversal are:
Same side exterior angles, which are said to be supplementary, that is, they have a sum that equals 180 degrees.Vertical angles which are equal in measure.Same side interior angles are usually equal to each other.Linear pair which have a sum of 180 degrees.Using angle relationships, the following angle measures are determined as follows:
a = 180 - 62 = 118° [same side exterior angles]
b = a [vertical angles]
b = 118°
c = 180 - 148 [Linear pair]
c = 32°
d = 2 [same side interior angles]
d = 32°
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PLS HELP ASAP (100 POINTS) The line of best fit for the following data is represented by y = 0.81x + 6.9.
x y
3 9
6 9
5 13
7 13
8 16
8 11
What is the sum of the residuals? What does this tell us about the line of best fit?
A. 0.37; This indicates that the line of best fit is not very accurate and is a good model for prediction.
B. −0.37; This indicates that the line of best fit is accurate and is an overall a good model for prediction.
C. 0; This indicates that the line of best fit is very accurate and a good model for prediction.
D. 0; This indicates that the line of best fit is not very accurate and is not a good model for prediction.
Answer:
B. −0.37; This indicates that the line of best fit is accurate and is an overall good model for prediction.Step-by-step explanation:
y = 0.81x + 6.9
residual value = Measured value - Predicted value
Measured value = actual y-coordinate of the point, y
Predicted value = value of y from the equation, y1
residual value = (actual y-coordinate of the point, y) - (value of y from the equation, y1)
residual value = y - y1
x y y1 residual (y-y1)
3 9 9.33 -0.33
6 9 11.76 -2.76
5 13 10.95 2.05
7 13 12.57 0.43
8 16 13.38 2.62
8 11 13.38 - 2.38
Sum of residuals:
sum = (-0.33) +(-2.76)+(2.05)+(0.43)+(2.62)+(-2.38)
sum of residuals = -0.37ANSWER:
B. −0.37; This indicates that the line of best fit is accurate and is an overall good model for prediction.
(Though not very accurate as it should have been if the sum of residuals was equal to 0).
A total discrepancy of -0.37 is not too bad.
Answer:Answer:
B. −0.37;
This indicates that the line of best fit is accurate and is an overall good model for prediction.
Step-by-step explanation:
y = 0.81x + 6.9
residual value = Measured value - Predicted value
Measured value = actual y-coordinate of the point, y
Predicted value = value of y from the equation, y1
residual value = (actual y-coordinate of the point, y) - (value of y from the equation, y1)
residual value = y - y1
x y y1 residual (y-y1)
3 9 9.33 -0.33
6 9 11.76 -2.76
5 13 10.95 2.05
7 13 12.57 0.43
8 16 13.38 2.62
8 11 13.38 - 2.38
Sum of residuals:
sum = (-0.33) +(-2.76)+(2.05)+(0.43)+(2.62)+(-2.38)
sum of residuals = -0.37
ANSWER:
B. −0.37; This indicates that the line of best fit is accurate and is an overall good model for prediction.
(Though not very accurate as it should have been if the sum of residuals was equal to 0).
A total discrepancy of -0.37 is not too bad.
the question is the png
The slope of the line parallel to y = 4 / 7 x + 7 is 4 /7.
The slope of the line perpendicular to y = 4 / 7 x + 7 is - 7 / 4.
How to find lines that are parallel and perpendicular?The equation of a line can be described as follows:
y = mx + b
where
m = slopeb = y-interceptThe equation of the line given is y = 4 / 7 x + 7.
Parallel lines have the same slope.
Therefore, the slope of the line parallel to the given equation of the line is 4 / 7.
A line perpendicular to each other follows the rule below:
m₁ m₂ = -1
where
m₁ = first slopem₂ = second slopeTherefore, let's find the slope of the line perpendicular to the given equation.
4 / 7 m₂ = -1
cross multiply
4m₂ = -7
m₂ = - 7 / 4
Therefore, the slope of the line perpendicular to the equation is - 7/4
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Given the 2 statements: "If you study for your test, then you will pass
your test," and "If you passed your test, then you studied for your
test." the biconditional is:
The biconditional statement is "You study for your test if and only if you passed".
What is biconditional statement?
A biconditional statement combines a conditional statement with its opposite expressed in the form of "if and only if."
The given statements are,
"If you study for your test, then you will pass your test" and "you passed your test then you studied for your test".
The biconditional statement is: "You study for your test if and only if you passed".
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the repair time for air conditioning units is believed to have a normal distribution with a mean of 38 minutes and a standard deviation of 12 minutes. find the probability that the repair time for an air conditioning unit will be between 29 and 44 minutes.
The probability that the repair time for an air conditioning unit will be between 29 and 44 minutes is 0.4648
We are given:
u= 38,s = 12
We have to find P(29 < x< 44)
Using the z-score formula, we have:
P(29 <x <44) = P(-0.75 < z <0.5)
Using the standard normal table, we have:
P(29 <x<44) = P(-0.75 < z < 0.5) = 0.4648
Therefore, the probability that the repair time for an air conditioning unit will be between 29 and 44 minutes is 0.4648
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Which is another way to represent
five hundred six and ninety-two
thousandths?
Select all that apply.
(5 x 100) + (6 × 1)
+ X
(9 × 10) + (2x 100)
(5 x 100) + (6 × 1)
+(9 × 100) + (2.× 1,000)
506.092
506.902
506.92
a+b=0
What does b equal
Answer: D) -a
Step-by-step explanation:
a+b=0 , add -a for both side
- a + a + b = 0 - a
we cancel (- a + a) and we get
b = 0 - a => b = -a
Answer:
option d -a
if you take a to the opposite side of the equal mark it's sign is going to change since it's positive it's going to be negative on the other side 0 -a = -a
baam answer
suppose that a tall child with arm span 120 cm and height 118 cm was added to the sample used in this study. what effect will this addition have on the correlation and the slope of the least-squares regression line?
A tall child with an arm span of 120 cm and height of 118 cm was added to the sample used in this study then the correlation will increase whereas the slope stays the same.
Correlation is a relation between two variables, by shifting one independent variable, how the dependent variable will shift, that's the degree of correlation since Correlation can be fitted in any shape or condition. It can be fitted nonlinear, straight or curvy straight, etc whereas slope is related to a straight variety of two variables, it is characterized as the rate of altering of the dependent variable in order with the independent variable. By and large you'll discover equation incline =( y2-y1)/(x2-x1).
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Solve each system of the new equations by adding or subtracting
Given the equations
x + y = 5----------------------(1)
x - 3y = 3-----------------------(2)
Subtract equation (2) from (1)
x - x -3y - y = 3 - 5
-4y = -2
Divide both -4
[tex]\begin{gathered} \frac{-4y}{-4}\text{ = }\frac{-2}{-4} \\ y\text{ = }\frac{1}{2}\text{ = 0.5} \\ \end{gathered}[/tex]Substitute y = 1/2 into equation (1)
x + y = 5
[tex]\begin{gathered} x\text{ + }\frac{1}{2}\text{ =5} \\ x\text{ = 5 -}\frac{1}{2} \\ x\text{ = }\frac{10-1}{2} \\ x=\frac{9}{2}\text{ = 4.5} \\ \end{gathered}[/tex]Hence, the solution to the equations is
[tex]\begin{gathered} x\text{ = }4.5,\text{ y = 0.5} \\ Or\text{ in coordinate form, (4.5, 0.5)} \end{gathered}[/tex](6-6)x 6=0
(6 + 6):6=2
6? 6?6 = 4
Answer:
I don't know if you can use permutations but
(6P2-6)/6=4 ????
WRITE A SIMPLIFIED EXPRESSION FOR THE PERIMETER OF THE TRIANGLE.
The simplified expression of the perimeter of the triangle is 3.75x - 7.
How to find the perimeter of a triangle?A triangle is a a polygon with three sides. The sum of angles in a triangle is 180 degrees.
The perimeter of a triangle is the sum of the whole three sides.
Therefore, the simplified expression that represents the perimeter of the triangle is as follows:
Hence, the three sides of the triangle are as follows;
1.5x - 31.5x - 30.75x - 1Hence,
perimeter of the triangle = 1.5x - 3 + 1.5x - 3 + 0.75x - 1
perimeter of the triangle = 1.5x + 1.5x + 0.75x - 3 - 3 - 1
perimeter of the triangle = 3.0x + 0.75x - 7
perimeter of the triangle = 3.75x - 7
Therefore, the simplified expression is 3.75x - 7
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(25)!!!!!
Two sidewalks in a park are represented by lines on a coordinate grid. Two points on each of the lines are shown in the tables.
Sidewalk 1
x y
2 7
0 3
Sidewalk 2
x y
1 5
3 3
(a)Write the equation for Sidewalk 1 in slope-intercept form.
(b)Write the equation for Sidewalk 2 in point-slope form and then in slope-intercept form.
(c)Is the system of equations consistent independent, coincident, or inconsistent? Explain.
(d)If the two sidewalks intersect, what are the coordinates of the point of intersection? Use the substitution method and show your work.
Helpppppp!! answer it who takes this test
Using linear functions, it is found that:
a) The equation is: y = 2x + 3.
b) The equations are:
Point - slope form: y - 5 = -(x - 1).Slope - intercept form: y = -x + 6.c) The systems are consistent independent.
d) The point of intersection is (1, 5).
Linear functionA linear function is defined in slope-intercept formula by the rule presented as follows:
y = mx + b.
In which:
m is the constant rate of change of the function, called slope.b is the value of y when x = 0, called intercept.For Sidewalk 1, it is found that:
When x increases by 2, y increases by 4, hence the slope is of m = 2.When x = 0, y = 3, hence the intercept is of b = 3.Then the rule is:
y = 2x + 3.
For Sidewalk 2, when x changes by 2, y decays by 2, hence the slope is:
m = -2/2 = -1.
The line goes through point (1,5), hence the equation in point-slope form is:
y - 5 = -(x - 1).
Combining the like terms, the slope-intercept form is:
y - 5 = -x + 1
y = -x + 6.
Since the two lines have different slopes, the system is consistent independent.
The x-coordinate of the intersection is:
-x + 6 = 3 + 2x.
3x = 3
x = 1.
The y-coordinate is:
-x + 6 = -1 + 6 = 5.
Hence the intersection point is:
(1, 5).
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Answer: I am I don't know man
Step-by-step explanation: answer is I don't know.
Rajesh obtain 93 marks in English out of 100 marks but Sita obtained 82 marks.Convert their marks in a fraction and calculate who got more marks?How many parts more marks then other.Also write their grade by asking with your teacher
Answer:
Answer 1: Rajesh: 93/100 Sita: 82/100 (simplest form: 41/50) Rajesh earned more.
Answer 2: 11/100 more marks
Answer 3: Rajesh got an A, while Sita got a B-
Step-by-step explanation:
Put the 93 on top of 100, and do the same for 82.
Rajesh clearly earned more. Subtract 82 from 93 to find out Rajesh score 11 points more.
xThe number of hours of daylight in a city in the Northern hemisphere shows periodic behavior over time.• The average number of daylight hours is 12.• The maximum number of daylight hours is 14.4.• The period is 365 days.• The day with the least sunlight is December 20.Which equation models the number of hours of daylight on the day that comes t days after the shortest day of the previous year?
EXPLANATION
Since we know that the number of hours is represented by a periodic function, the appropriate model is the sine function.
As the average number of daylight hours is 12 with a maximum and minimum of 14.4 and 9.6 respectively.
Furthermore, the period is 365.
Thus, the period is as follows:
[tex]\frac{2\pi}{365}=0.017[/tex]The appropiate model is the following:
[tex]H(t)=a\sin(0.017t)+12[/tex]Now, we need to compute the value of a:
Since the sine function reaches its highest value at t=90° and is represented by 14.4, when t=90°, the value of the function is asin(0.017t) = 1
Therefore,
14.4 = a + 12
Subtracting -12 to both sides:
14.4 - 12 = a
Subtracting numbers:
2.4 = a
In conclusion, the final function is the following:
[tex]H(t)=2.4\sin(0.017t)+12[/tex]Since the minimum is at t=0, we want:
[tex]H\left(t\right)=-2.4cos\left(0.017t\right)+12[/tex]In conclusion, the solution is the OPTION C)
Identify the rule for fg when f(x) = –3x – 6 and g(x) = x2 – x – 6.
The rule for the given function f /g when the function f(x) = -3x -6 and
g(x) = x² -x - 6 is identified as f(x) / g(x) = -3 / (x -3).
As given in the question,
Given function are:
f(x) = -3x -6
g(x) = x² -x - 6
Rule to identify for the function f(x) / g(x) we get,
Substitute the value of f(x) and g(x) in the required rule we have,
f(x) / g(x) = (-3x -6 ) / ( x² -x - 6 )
Now simplify the function to get the rule:
f(x) / g(x) = -3(x+2) / (x² -3x +2x -6)
⇒ f(x) / g(x) = -3(x+2) /(x-3)(x+2)
⇒ f(x) / g(x) = -3 / (x-3)
Therefore, the rule for the given function f /g when the function f(x) = -3x -6 and g(x) = x² -x - 6 is identified as f(x) / g(x) = -3 / (x -3).
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3y=26-5x put into the simplest y=mx+b form
Answer:
y=-5x/3+26/3
Step-by-step explanation:
Because we want the equation to look like y=mx+b, rearrange the terms.
Since 26-5x is the same as -5x+26, rewrite it like that.
3y=-5x+26
Now, since we want the value of y, divide by 3 on both sides.
3y/3=y
-5x/3= -5x/3
26/3= 26/3
The simplest form would look like:
y=-5x/3+26/3