Answer:
C
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
To obtain either equation we require to know both the slope and one ordered pair that lies on the line.
solve the absolute value equation
2 = |x|-1
If you're looking for x, then:
2 = |x|-1
lxl-1 = 2
lxl-1+1=2+1
lxl=3
so x = -3, x=3
In 6 minutes, a conveyor belt moves 300 pounds of recyclable aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 18 minutes. If both belts are used, find how long it takes to move the cans to the storage area.
If we use both belts, it takes 4.5 minutes to carry the can to the storage area.
Let's assume, t = time required to move 300 pounds using both belts.
For this first calculate the speed or mass flow rate of each conveyor belt.
The big one can do 300 pounds in 6 minutes, so its speed is 300 pounds/6 minutes = 50 pounds/minute.
The smaller one takes 18 minutes, so the speed is 300 pounds/18 min = 50/3 pounds/minute.
We can see that the combined speed of both machines when working together is 50 + 50/3 = 50 (1 + 1/3) = 50 x 4/3 = 200/3 pounds/minute.
Then we find that the two machines together can transfer 300 pounds in t = 300/200/3 = 300/200 x 3 = 4.5 minutes.
Alternate Method:
We can do that too
Let t = the time required to move 300 pounds on both belts.
Job completed = 1 (300 pounds moved)
t/6 + t/18 = 1
Taking L.C.M
=> (3t + t)/18 = 1
=> 4t/18 = 1
=> t = 4.5 minutes
Hence, it takes 4.5 minutes to carry the can to the storage area.
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Find the value of f(12) given the following arithmetic sequence of f(3) = -3 and f(6) = 8.
The value of f(12) in the arithmetic sequence is 30.
How to solve arithmetic sequence?Arithmetic sequence formula can be represented as follows;
aₙ = a + (n - 1)d
where
d = common differencea = first termn = number of termTherefore,
f(3) = - 3
f(6) = 8
Hence, let's find f(12).
-3 = a + 2d
8 = a + 5d
3d = 11
d = 11 / 3
a = -3 - 2(11 / 3)
a = - 3 - 22 / 3
a = - 31 / 3
Hence,
a₁₂ = a + 11d
a₁₂ = - 31 / 3 + 11(11 / 3)
a₁₂ = - 31 / 3 + 121 / 3
a₁₂ = 90 / 3
a₁₂ = 30
Therefore,
f(12) = 30
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I need help asap if molly buys 6 tickets and they cost 75 dollars in total how much would one cost?
y do i have to write so much for a small answer the answer is 12.5
Answer: One ticket would cost $12.50
Step-by-step explanation:
If 6 tickets cost $75, to find the cost of one ticket, we need to divide.
$75 divided by 6 is $12.5.
$12.5 is not a valid answer, so we need to show the hundredths place, which is 0. This means the answer is $12.50.
Write the equation of the line in fully simplified slope-intercept form.
The equation of the line as represented in the task content in fully simplified slope-intercept form is; y = -( 1/2 )x - 2.
Equation of a line in slope-intercept formIt follows from the task content that the equation of the given line in slope-intercept form is to be determined.
As evident on the graph, the y-intercept and x-intercept of the line are; (0, -1) and (-2, 0).
Therefore, the slope can be determined from the slope formula as;
m = ( 0 - (-1) ) / (-2 - 0)
m = 1 / -2 = -1 / 2.
Therefore, by simulation of the slope-intercept model of the equation of a straight line; y = mx + c where, m = slope and c = y-coordinate of the y-intercept;
The equation of the given line is;
y = -(1/2)x - 2.
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Pls help me fast rapidly on khan academy:
Answer:
This triangle is obtuse and isosceles
Step-by-step explanation:
An obtuse triangle is a triangle in which one of the angles is greater than 90°. You can clearly see that angle NPO is greater than a right angle.
An isosceles triangle is a triangle in which two sides are equal and two angles are equal. Sides NP and PO are equal because they both measure 4m, which necessarily means that the angles opposite them are congruent (angles PNO and NOP).
Answer:
ΔNOP is obtuse triangle and isosceles triangle.
Step-by-step explanation:
An acute triangle has three angles that each measure less than 90°.
An obtuse triangle is a triangle with one angle greater than 90°.
A right triangle is a triangle with one 90° angle represented by the symbol ∟.
From inspection of the triangle, it appears that angle P is greater than 90°, which means it is an obtuse triangle.
This can be confirmed by using the cosine rule to calculate angle P.
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Cosine Rule (for finding angles)} \\\\$\cos(C)=\dfrac{a^2+b^2-c^2}{2ab}$\\\\\\where:\\ \phantom{ww}$\bullet$ $C$ is the angle. \\ \phantom{ww}$\bullet$ $a$ and $b$ are the sides adjacent the angle. \\ \phantom{ww}$\bullet$ $c$ is the side opposite the angle.\\\end{minipage}}[/tex]
Therefore:
[tex]\implies \cos(P)=\dfrac{4^2+4^2-7^2}{2(4)(4)}[/tex]
[tex]\implies \cos(P)=-\dfrac{17}{32}[/tex]
[tex]\implies P=\cos^{-1}\left(-\dfrac{17}{32}\right)[/tex]
[tex]\implies P=122.08995...^{\circ}[/tex]
As 122.1° > 90°, this proves that triangle NOP is obtuse.
An equilateral triangle has three sides of equal length.
A scalene triangle has three sides of differing lengths.
An isosceles triangle has two sides of equal length.
Therefore, as NP = OP ≠ ON, the triangle has two sides of equal length and so it an isosceles triangle.
In a polygon one interior angle is 25 degrees.What is the size of the exterior angle next to (adjacent)11
In a polygon, the size of the exterior angle next to the adjacent is 155°
Exterior angle:
Exterior angle means the angle between any side of a shape, and a line extended from the next side
Given,
In a polygon one interior angle is 25 degrees.
Here we need to find the exterior angle next to the adjacent.
In order to find the exterior angle, we have to do the following,
We know that each interior angle of the polygon is 25 degrees, so each exterior angle of the polygon is
=> 180 - 25
=> 155°
Therefore, the measure of the exterior angle is 155°.
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The individual times of four members of a 4×400 m relay team are shown below find the teams total waste time in seconds
half a number less than 3 is at most 5. translate as a equation or inequality.
It will be written as inequality
3 - (x / 2) ≤ 5
Inequality is a mathematical relation which is use to make non-equal comparisons between equations or numbers.
Now let us look at the question.
Half a number less than 3. Let us suppose the number to be 'x' so
3 minus half of x which can be written as 3 - (x / 2)
Next it says that it is at most 5 which means it will be 5 or less than that.
Therefore we can easily write it as inequality 3 - (x / 2) ≤ 5
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Brittany has a home-based business making corsages and boutonnieres for school dances. Last year, she sold 12 corsages and 17 boutonnieres, which brought in a total of $621. This year, she sold 19 corsages and 16 boutonnieres, for a total of $754. How much does each item sell for?
please help
Each corsages sell for $22. And Each boutonnieres sell for $21.
Brittany sold 12 corsages and 17 boutonnieres last year in total of $621.
And she sold 19 corsages and 16 boutonnieres this year for a total of $754.
First, we will create the system of equation from given information
So, the equations are
12x+17y=621..…(1)
19x+16y=754..…(2)
Where,
X=cost of one corsage
Y=cost of one boutonniere
Make y the subject of equation (1)
y=(621-12x)/17
Put this value of y in equation (2)
Therefore
19x+16((621-12x)/17)=754
19x+(9936-192x)/17=754
(323x+9936-192x)/17=754
131x+9936=12818
131x=12818-9936
131x=2882
x=2882/131
x=22
So, the cost of one corsage is $22.
Now, put this value of x in equation (1)
12×22+17y=621
264+17y=621
17y=621-264
y=357/17
y=21
The cost of one boutonniere is $21.
Thus, the cost of each corsages and boutonnieres are $22 and $21.
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Choose the solution to this inequality.
3.5≥b+1.8
Answer:
[tex]1.7\geq b[/tex]
Step-by-step explanation:
3.5>=b+1.8
-1.8. -1.8
1.7>=b
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"A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is feet.
(Simplify your answer.)"
The time taken for the rocket to reach its maximum height is; 2.25 seconds.
The maximum height reached by the toy rocket whose initial velocity is; 72 feet per second is; 88 feet.
What is the maximum height reached by the rocket?It follows from the task content that the maximum height reached by the rocket is to be determined.
The given function is; h (t) = -16 t² + 72t + 7.
Since it follows from evaluation that; at maximum height, the rate of change of height to time is equal to 0.
Therefore; at maximum height;
h'(t) = 0
h'(t) = -32t + 72 = 0
-32t = -72
t = -72/-32
t = 2.25 seconds.
Therefore, the time taken for the rocket to reach its maximum height is; 2.25 seconds.
Also, the maximum height reached by the rocket is at; h (2.25);
h(2.25) = -16(2.25)² + 72 (2.25) + 7
= -81 + 162 + 7
= 88.
The maximum height reached is; 88 feet.
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19. MODELING In Example 6, 44% of the voters say they plan to reelect the mayor. The poll has a margin of error of ±3% percentage points. Use a model to write and solve an absolute value inequality to find the least and greatest percents of voters who plan to reelect the mayor.
The Least percentage point = 41
The Greatest percentage point = 47
What is percent?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.
Given:
Percentage of voters who plan to re-elect mayor = 44%
Margin of Error in measurement = ±3 % points
The absolute value inequality to find the lowest and greatest percent of points :
X = mid value
44% = estimated percentage
≤3 = error margin
Therefore,
|mid value - estimate| ≤ error margin
|x − 44| ≤ 3
⇒ -3 ≤ x - 44 ≤ +3
Add 44 on both sides,
-3 + 44 ≤ x ≤ 3 + 44
Simplifying,
41 ≤ x ≤ 47
Hence,
The Least percentage point = 41
The Greatest percentage point = 47
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What are the steps involved in the financial plann
Identify your Financial Situation,
Determine Financial Goals,
Identify Alternatives for Investment,
Evaluate Alternatives,
Put Together a Financial Plan and Implement,
Review, Re-evaluate and Monitor The Plan
What is financial planning?The process of figuring out how a corporation will be able to afford to meet its strategic goals and objectives is known as financial planning. Normally, a business develops a financial plan right away after deciding on its vision and goals. The Financial Plan details all the tasks, assets, tools, and supplies required to accomplish these goals as well as the timelines involved.
The following tasks are part of the financial planning activity:
Analyze the commercial environmentVerify the company's goals and vision.Determine the types of resources required to accomplish these goals.Measure the quantity of the resource (labor, equipment, materials)Determine the overall expense of each type of resource.Compile the expenses to make a budget.Determine any dangers and problems with the planned budget.To learn more about financial planning, refer to
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Equation for (-6,0) (0,-8)
The equation of the line passing through (-6,0) and (0,-8) will be y = -4x/3-8.
According to the question,
We have the following information:
We have two points: (-6,0) and (0,-8) and we have to find the equation.
We know that following formula is used to find the slope of the line:
m = (y2-y1)/(x2-x1)
In this case, we have x1 = -6, y1 = 0, x2 = 0 and y2 = -8.
m = (-8-0)/{0-(-6)}
m = -8/(0+6)
m = -8/6
Dividing this fraction by 2:
m = -4/3
Now, the following formula is used to find the equation of the line:
(y-y1) = m(x-x1)
y-0 = -4/3{x-(-6)}
y = -4/3(x+6)
y = -4x/3-8
Hence, the equation of the line passing through (-6,0) and (0,-8) will be y = -4x/3-8.
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What is the equation of the line that passes through the point (-4, -8) and hads a slope of
5/2
Answer:
y = 5/2x - 8
Step-by-step explanation:
URGENT! Please Help!
The values of x or y are as follows:
(a) y = 4
(b) x = -2
(c) y = 6
(d) x = 3
(a) Given, that a line passes through (-3 , y) and (-9 , -2) having slope m = 1
as, we know the formula of slope i.e. (y1 - y2)/(x1 - x2) = m
So, (y + 2)/(-3 + 9) = 1
= (y + 2)/6 = 1
= y + 2 = 6
So, y = 4
(b) Given, that a line passes through (x , -7) and (1 , 2) having slope m = 3
as, we know the formula of slope i.e. (y1 - y2)/(x1 - x2) = m
So, (-7 - 2)/(x - 1) = 3
= -9/(x - 1) = 3
= x - 1 = -3
So, x = -2
(c) Given, that a line passes through (9 , y) and (3 , 2) having slope m = 2/3
as, we know the formula of slope i.e. (y1 - y2)/(x1 - x2) = m
So, (y - 2)/(9 - 3) = 2/3
= (y - 2)/6 = 2/3
= y - 2 = 4
So, y = 6
(d) Given, that a line passes through (7 , 5) and (x , 2) having slope m = 3/4
as, we know the formula of slope i.e. (y1 - y2)/(x1 - x2) = m
So, (5 - 2)/(7 - x) = 3/4
= 3/(7 - x) = 3/4
=7 - x = 4
So, x = 3
Hence, the values of x or y are as follows:
y = 4 , x = -2 , y = 6 and x = 3.
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The number of newly reported crime cases in a county in New York State is shown in the accompanying table, where x represents the number of years since 2011, and y represents number of new cases. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest hundredth. Using this equation, estimate the calendar year in which the number of new cases would reach 1141.
The linear regression equation that represents this set of data is given by:
y = 30x + 854.6.
The predicted calendar year in which the number of new cases would reach 1141 is:
2020.
How to obtain the linear regression equation?The format of the linear regression equation is given as follows:
y = mx + b.
In which the coefficients are listed as follows:
m is the slope.b is the y-intercept.The equation is built inserting the points given on the table into a linear regression calculator.
The points from the table given by the image at the end of the answer are given as follows:
(0, 856), (1, 871), (2, 924), (3, 961), (4,961).
Inserting these points into a calculator, the equation is given as follows:
y = 30x + 854.6.
The predicted calendar year in which the number of new cases would reach 1141 is 2011 + integer part of x, when y = 1141, hence:
1141 = 30x + 854.6
x = (1141 - 854.6)/30
x = 9.54.
Hence during the year of 2020.
Missing InformationThe table is given by the image shown at the end of the answer.
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A bag contains 15 green, 18 yellow, and 16 orange balls.
One ball is randomly selected. To the nearest percent, what is the probability of the event?
P(yellow)=
31%, 33%, 37%, and 42%
The probability of the event P(Yellow) is 37% , the correct option is (c) .
In the question ,
it is given that
number of green balls in the bag [tex]=[/tex] 15
number of yellow balls in the bag [tex]=[/tex] 18
number of orange balls in the bag [tex]=[/tex] 16
So , total number of balls in the bag = number of green balls + yellow balls + orange balls .
On substituting the values ,
we get
total number of balls = 15 +18 + 16 = 49
the probability of the event P(Yellow) = (number of yellow balls)/(total balls)
= 18/49
= 0.3673
= 36.73%
≈ 37%
Therefore , The probability of the event P(Yellow) is 37% .
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Simplify
this question
Answer:
1/4
Step-by-step explanation:
[tex]\frac{6 - \sqrt{25} }{4}[/tex] =
[tex]\frac{6-5}{4}[/tex] =
[tex]\frac{1}{4}[/tex]
find x in angle ABC
............
Answer: The value of x in ∆ ABC is
Step-by-step explanation: By AA similarity
x² = 4* 16
x = 8
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The Houston Armadillos, a minor-league baseball team, play their weekly games in a small stadium just outside Houston. The stadium holds 10,000 people and tickets sell for $10 each. The franchise owner estimates that the team's annual fixed expenses are $180,000, and the variable expense per ticket sold is $1. (In the following requirements, ignore income taxes.)
Answer:
Required
1. What is the break-even point in tickets?
2. How many tickets must be sold to earn a profit of $30,000?
3. How many tickets must be sold to earn a profit of $100,000?
Step-by-step explanation:
IXL help FAST PLEASE !
Answer:
x=9
Step-by-step explanation:
these 2 angles are equivalent so we set them equal to each other
124-x=8x+43
81-x=8x
81=9x
9=x
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Triangle X Y Z is shown. Angle X Z Y is a right angle. Angle Z X Y is 60 degrees and angle X Y Z is 30 degrees. The length of hypotenuse X Y is 4.
Given right triangle XYZ, what is the value of tan(Y)?
The value of Tan Y is 0. 8660
How to determine the identityFrom the information given, we have that;
XZY = 90 degreesZXY = 60 degreesXYZ = 30 degreesXY = 4Now, let's determine the value of the adjacent side
cos θ = adjacent/ hypotenuse
cos 60 = adjacent/ 4
Adjacent = 2
Using Pythagorean theorem
4² = 2² + c²
16 - 4 = c²
c = √12
c = 3. 5
Tan Y = 3. 5/ 4
Tan Y = 0. 8660
Hence, the value is 0. 8660
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Answer:b
Step-by-step explanation:
At the end of a snow storm, Audrey saw there was a lot of snow on her front lawn.
The temperature increased and the snow began to melt at a steady rate. There was a
depth of 10 inches of snow on the lawn when the storm ended and then it started
a melting at a rate of 2 inches per hour. Write an equation for S in terms of t,
snow
representing the depth of snow on Audrey's lawn, in inches, t hours after the snow
stopped falling.
An equation that represents the depth of snow on Audrey's lawn, in inches, t hours after the snow stopped falling is S = 10 - 2t
In this question, there was a depth of 10 inches of snow on the lawn when the storm ended and then it started a melting at a rate of 2 inches per hour.
We need to write an equation for S in terms of t, snow representing the depth of snow on Audrey's lawn, in inches, t hours after the snow stopped falling.
So, the equation would be,
S = 10 - 2t
Therefore, an equation that represents the depth of snow on Audrey's lawn, in inches, t hours after the snow stopped falling is S = 10 - 2t
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leaves Rockford, Illinois, at the rate of 70 mph, bound for Madison, Wisconsin. At the same time, a truck leaves Madison at the rate of 50 mph, bound for Rockford. If the cities are 72 miles apart, how long will it take for the car and the truck to meet?
The time taken for the car and truck to meet is 36 minutes.
What are speed and time?The relationship between the three variables is the fundamental concept of speed, time, and distance.A body's speed is defined as the distance travelled per unit of time. That is, speed = distance divided by time.The time for the car and the truck must be the same.
time = distance/rateLet "x" be the car'sdistance:
Then 72-x is the truck'sdistancetime = timeNow,
=> x/70 = (72-x)/50=> 50x = 5040-70x=>50x+70x = 5040=> 120 x = 5040=> x = 5040/120 = 42 miles.Then trucks distance:
=> 72-42=30 miles.Time is:
=> 42/70 = 0.6 hrs=> 0.6*60 = 36 minutes.Hence, the time taken for the car and truck to meet is 36 minutes.
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Biologists estimate that the number of deer in Rhode Island in 2003 was 1,028, and in 2008 it had grown to 1,488. Biologists would like to model the deer population, p, as a function of the years, t, since 2000.
(a) Represent the information we have been told as two coordinate points. Be careful to know what your values of time are for each year.
(b) Calculate ∡p ÷ ∡t from 2003 to 2008. Include proper units in your answer.
(c) Give a physical interpretation of the value you found in part (b).
(d) Determine a linear relationship between the deer population, p, and the years since 2000, t.
(e) How many deer does this model predict were in Rhode Island in the year 2000? What does this represent about the linear function?
(f) How many deer does the model predict for Rhode Island now?
a) The points are given as follows: (3, 1028) and (8, 1488).
b) The rate of change is:
c) The interpretation of the rate of change is that it gives the yearly increase in the number of deers.
d) The equation is: y = 92x + 752.
e) The prediction for the year of 2000 is the intercept of the function, which is of 752 deer.
f) The prediction for the current year of 2022 is of 2776 deer.
What is a linear function?The slope-intercept representation of a linear function is:
y = mx + b
The coefficients of the function and their meaning in the context of this problem are listed as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x increases by one. Hence, in this problem, it represents the yearly increase in the number of deer.b is the y-intercept of the function, which is the value of the function when it's graph crosses the y-axis, that is, when x = 0. Hence, in this problem, it gives the population of deer in the year of 2000.Considering the reference year 2000 as year 0, the coordinate points of the function are given as follows:
(3, 1028), (8, 1488).
Given two points, the slope of the function is given by the change in the output divided by the change in the input, hence:
m = (1488 - 1028)/(8 - 3) = 92.
Hence the function is:
y = 92x + b.
When x = 3, y = 1028, hence the intercept b is obtained as follows:
1028 = 92(3) + b
b = 1028 - 92(3)
b = 752.
Then:
y = 92x + 752.
2022 is 22 years after 2000, hence the estimate for the number of deer is given as follows:
y = 92(22) + 752 = 2776.
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24. the numbers in a sequence
Variable
Term
Difference
Evaluate
Exponent
Answer:
34
Step-by-step explanation:
I will need a lot more info then that but i think it'll be 34
Find the measure of the requested angle.
d =
e =
Answer:
e is 63 degrees
d is 31 degrees
Determine which set of side measurements could be used to form a triangle.
2, 6, 10
3, 18, 22
7, 13, 16
8, 7, 19
The set of side measurements could be used to form a triangle is 7, 13 and 16.
If a, b and c are the sides of the triangle
Then
a+b > c
b+c > a
c+a > b
The first set of side measurements = 2, 6 and 10
2+6 > 10
8 < 10
This is not the side measurements of a triangle
The second set of side measurements = 3, 18 and 22
3+18 > 22
21 < 22
The is not the side measurements of a triangle
The third set of side measurements = 7, 13, 16
7+13 > 16
20 > 16
13+16 > 7
29 > 7
7+16 > 12
23 >12
This is the side measurements of a triangle
The fourth set of side measurements = 8, 7 and 19
8+7 > 19
15 < 19
This is not the side measurements of a triangle
Hence, the set of side measurements could be used to form a triangle is 7, 13 and 16
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Answer:
C. 7, 13, 16
Step-by-step explanation:
In order to be a triangle, the two smaller sides need to add up and be greater than the 3rd side.
In all the other sides they end up shorter:
2 + 6 = 8
8 < 10
3 + 18 = 21
21 < 22
8 + 7 = 15
15 < 19
BUT
7 + 13 = 20
20 > 16
