A car is driving away from El Paso with constant velocity. At 1 p.m., it is 145 miles away from El Paso. At 3 p.m., it is 275 miles away from El Paso.
Part A: Write a linear function that describes the distance (in miles) the car is from El Paso in terms of time (in hours after 12:00 p.m.).
The linear function that describes the distance (in miles) is therefore y = 65x + 80
How to solve for the linear functionWe have to find the slope and the intercept in other to get the linear function
The data points are:
(1, 145) and (3, 275).
m = (y2 - y1) / (x2 - x1)
fixing the data points we have
m = (275 - 145) / (3 - 1)
= 130 / 2
= 65
y = mx + b
(1, 145):
145 = 65(1) + b
b = 145 - 65
= 80
y intercept is 80
The linear function is therefore y = 65x + 80
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82°
118°
95°
X°
Image not to scale
Calculate the missing angle x.
Answer:
x = 65
Step-by-step explanation:
the sum of the interior angles of a quadrilateral = 360°
sum the angles and equate to 360
x + 95 + 118 + 82 = 360
x + 295 = 360 ( subtract 295 from both sides )
x = 65
60% of the books in a library are for adults, 5% are for young people and the rest are for children. If there are 280 books for children, how many books are there altogether?
Answer:
800 books
problem solving steps:
adults:60%
young people:5%
children=100%-60%-5%
=35%
35%=280 books
1%=280÷35
=8
100%=800
so,there are 800 books
In each rule , copy the chart and fill in the missing parts
Answer:
7. 14
15. 30
28. 56
32. 64
18 36
x 2x
1/2y. y
2x. 4x
x+3 2x+9
Step-by-step explanation:
each out is double the in
classifying paralelagrams
a. Length of GK = \(\sqrt{34}\) and Length of adjacent to GK = \(\sqrt{34}\)
b. Slope of GK = \(\frac{5}{3}\) and Slope of adjacent to RS = \(-\frac{3}{5}\)
c. The parallelogram GHJK is Square.
Define the term parallelogram?A quadrilateral with two sets of parallel sides is referred to as a parallelogram. As a result, a parallelogram's opposite sides are parallel and congruent in length, and its opposite angles are similarly congruent.
Given in figure GHJK, the vertices are G(-3, 6), H(2, 3), J(-1, -2), K(-6, 1)
a. Length of line = \(\sqrt{({x_{2}-x_{1})^{2} } + ({y_{2}-y_{1})^{2}}\)
for points G(-3, 6) and K(-6, 1)
Length of GK = \(\sqrt{(-6+3)^{2} + (1-6)^{2} }\) = \(\sqrt{34}\)
Length of GK = \(\sqrt{34}\)
Length of adjacent side (GH, KJ) to GK = \(\sqrt{(2+3)^{2} + (3-6)^{2} }\) = \(\sqrt{34}\)
Length of adjacent to GK = \(\sqrt{34}\)
b. \(Slope = \frac{(y_{2} -y_{1})}{(x_{2} -x_{1})}\)
Slope of GK = \(\frac{(1 - 6)}{(-6 + 3)}\) = \(\frac{5}{3}\)
Slope of GK = \(\frac{5}{3}\)
Slope of adjacent side to GK = \(\frac{3-6}{2+3}\) = \(-\frac{3}{5}\)
Slope of adjacent to RS = \(-\frac{3}{5}\)
c. All sides are equals to \(\sqrt{34}\)
So, length of diagonal GJ = \(\sqrt{({-3+1))^{2} } + ({6+2})^{2}} = \sqrt{68}\)
and length of diagonal HK = \(\sqrt{({2+6))^{2} } + ({3-1})^{2}} = \sqrt{68}\)
All sides and diagonals are equal then parallelogram GHJK is Square.
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23% of 200 model please
Answer:46
Step-by-step explanation:
Answer:
200*23/100=46
Step-by-step explanation:
Hope it helps
Autumn went shopping for a new pair of sneakers the listed price of the pair of sneakers was $22 but the price with tax came to $23.98 find the percent sales tax
The percent sales tax of the shopping is 9%
How to find the percent sales taxFrom the question, we have the following parameters that can be used in our computation:
Sneakers = $22
Price with tax = $23.98
Using the above as a guide, we have the following:
Sales tax = (Price with tax - Sneakers)/Sneakers
Substitute the known values in the above equation, so, we have the following representation
Sales tax = (23.98 - 22)/22
Evaluate
Sales tax = 9%
Hence, the sales tax is 9%
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If you roll a six-sided die three times, how many possible outcomes are there?
Answer:
There would be 216 possible outcomes
Step-by-step explanation:
wn measures (Example 1)
B 8 in.
2.
85%
12 in.
A 35°
14 in.
60°
C
Z
42 in.
t
S
Y
36 in.
Answer:
The answer is A
Step-by-step explanation:
took the test.
The instructor noted the following scores on the last quiz of the semester for 8 students. Find the range of this data set 59,61,83,67,81,80,81,100
answer: the range is 41.
to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.
then we subtract the minimum from the maximum.
59 - 100 = 41.
Drag the measurements to the containers to show equal length
The measurements that show equal length exists 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft
What is meant by measurements?The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently.
An equation exists an expression that indicates the relationship between two or more numbers and variables.
1 ft = 12 in; 1 yd = 3 ft and 1 yd = 36 in.
Hence:
15 yd = 15 yd × 36 in per yd = 540 in
195 ft = 195 ft × 12 in per ft = 2340 in
5280 yd = 5280 yd * 3 ft per yd = 15840 ft
The measurements that show equal length exists 15 yd and 540 in, 195 ft and 2340 in, 5280 yd and 15840 ft.
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What is the value of √0? Explain your reasoning
The baseball team needs new bats. Their recent order is for 100 new bats. Bats are heavy, so they can only put 12 bats in a box. How many boxes do they need for the order? Does the remainder matter?
the baseball team needs 9 boxes for the order.
how to find number of boxes?if the baseball team needs 100 new bats and can only put 12 bats in a box, we can find the number of boxes they need by dividing the total number of bats by the number of bats per box:
100 / 12 = 8.33
We must round to the nearest whole number because we cannot have a fraction of a box. Therefore, the baseball team must order 9 boxes.
If the team wants to make sure they get all the bats they ordered, the remaining 0.33, which represents the four bats that can't fit in a complete box, is important. They could either arrange an additional container to oblige the excess bats, or they could contact the provider to check whether they can buy simply 4 extra bats to finish their request.
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The slope of the line below is -4. Which of the following is the iS point-slope
form of the line?
\ (2, -8)
O A. y+ 8 = -4(x-2)
O B. y+ 2 =-4(x-8)
• C. y-8 = -4(x+ 2)
• D. y- 2=-4(x+ 8)
Correct option is A, the iS point-slope form of the line is y+ 8 = -4(x-2). A straight line's equation can be written as both a point slope form and a slope intercept form.
What does "point-slope form of the line" refer to?A line equation written using a single line point and the slope of the line is the simplest definition of the term "point-slope form." The slope is expressed in point form as the ratio of the change in y values to the change in x values, also known as the rise over run (x, y).
The point slope form is useful when there is a slope and one or more points are present. Standard form is often easier to employ while doing algebraic computations. Depending on our needs or our level of expertise, we can alter the form of an equation. Both the point slope form and the slope intercept form can be used to express the equation for a straight line. The point slope form highlights any point on the line as well as the slope. The slope and y-intercept of a line are only shown in slope intercept form.
Given,
the slope of line = - 4 and point = (2,-8)
The equation of line = y - yo = m (x - xo)
where m = slope and x,y are coordinates
y + 8 = - 4 (x - 2)
y + 8 = - 4x + 8
y = - 4x
Therefore, the correct answer is option A, y+ 8 = -4(x-2)
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Jackie drinks a bottle of water and a bottle of orange juice every morning.
The bottle of water has 16.9 ounces. The bottle of orange juice has 15.2 ounces.
Which is the best estimate for the total amount Jackie drinks in the morning for an entire week
and gives a good explanation for that estimate?
Answer:
15.30
Step-by-step explanation:
use code tiko
Answer:
ayo what
Step-by-step explanation:
I 0 ×I 1× I 2 ×I 3×I 4
Answer:
the answer is twelve by multiplying them all.
Answer:
2 , 40,420
Step-by-step explanation:
10 × 11 × 12 × 13 × 14
1,320 × 182
2,40,240
Which of the following could be the ratio between the lengths of the two legs
of a 30-60-90 triangle?
Check all that apply.
A. √2:2
B. √√3:√√3
C. √5:3
D. 1 √3
□ E. 1: √2
O F. 2:3
SUBMIT
Answer: E
Step-by-step explanation:
The constraints of a problem are listed below. What are the vertices of the feasible region? 2x+3y≥12 5x+2y≥15 x ≥ 0 y ≥ 0
The vertices of the feasible region are (0 , 15/2) , (21/11 , 19/11) and (6 , 0)
Given, the constraints of a problem
2x+3y≥12
5x+2y≥15
x ≥ 0
y ≥ 0
On solving the equations, we get
( 2x + 3y ≥ 12 ) × 2
( 5x + 2y ≥ 15 ) × 3
4x + 6y ≥ 24
15x + 6y ≥ 45
On subtracting, we get
11x ≥ 21
x ≥ 21/11
x = 21/11
On putting the value of x, we get
42/11 + 3y = 12
y = 19/11
Hence, the vertices of the feasible region are (0 , 15/2) , (21/11 , 19/11) and (6 , 0)
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Select all the correct locations on the table. Select all of the complex numbers in the given table.
Answer:
answer in picture
Step-by-step explanation:
An artist has prepared a canvas on a
rectangular frame that is 3 inches by
4 inches: What is the area, in square
inches, of the canvas?
The area of the canvas is 12 square inches and the minimum selling price is (a) $1.30
What is the area of the canvas?Here, we have
A rectangular frame that is 3 inches by 4 inches:
This means that
Base = 3 inchesHeight = 4 inchesSo, we have
Area = Base * Height
So, we have:
Area = 3 * 4
Evaluate
Area = 12
Hence, the area, in square inches, of the canvas is 12 sq inches
Calculating the minimum selling priceStart by calculating the Revenue using
Profit = Revenue - Cost
Where
Profit = 420
Cost = 400 * 0.25 = 100
So, we have
Revenue - 100 = 420
Revenue = 520
For the minimum selling price, we have
Minimum = Revenue/Number of brownies
So, we have
Minimum = 520/400
Evaluate
Minimum = 1.30
Hence, the minimum selling price is $1.30
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Miguel plots points A, B, and C in the coordinate plane.
A. What is the distance between points A and B? Explain your reasoning.
B. Is (gif triangle) ABC an equilateral triangle? Explain your reasoning.
is △ABC equilateral? well, we dunno, however let's check for all sides' length.
\(~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{-6}~,~\stackrel{y_2}{-2}) ~\hfill AB=\sqrt{(~~ -6- (-3)~~)^2 + (~~ -2- 2~~)^2} \\\\\\ ~\hfill AB=\sqrt{( -3)^2 + ( -4)^2} \implies AB=\sqrt{ 25 }\implies \boxed{AB=5}\)
\(B(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad C(\stackrel{x_2}{0}~,~\stackrel{y_2}{-2}) ~\hfill BC=\sqrt{(~~ 0- (-6)~~)^2 + (~~ -2- (-2)~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 6)^2 + ( 0)^2} \implies BC=\sqrt{ 36 }\implies \boxed{BC=6} \\\\\\ C(\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\qquad A(\stackrel{x_2}{-3}~,~\stackrel{y_2}{2}) ~\hfill CA=\sqrt{(~~ -3- 0~~)^2 + (~~ 2- (-2)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -3)^2 + (4)^2} \implies CA=\sqrt{ 25 }\implies \boxed{CA=5}\)
well, not quite.
PLEASE HELP!!
. Three people are sitting on a bus. Kenji is directly behind Rita and directly left of Franco. If Rita and Kenji
are 4 feet apart, and Franco and Rita are 4.7 feet apart, what is the distance between Kenji and Franco? If
necessary, round to the nearest tenth.
the distance between Kenji and Franco is approximately 1.9 feet (rounded to the nearest tenth).
How often should you visit your courses
In D2L
It is recommended that you visit your courses on D2L frequently, ideally at least once a day, to stay up-to-date with any new announcements or assignments posted by your instructor. This will help you stay on track with your coursework and prevent you from falling behind. Additionally, regular visits to your courses can help you participate in discussions with your peers and ask questions if you are unsure about any of the material. It's important to remember that online learning requires a high level of self-discipline and responsibility, so making a habit of checking in on your courses regularly can contribute to your overall success in the class.
PLEASE HELP AND ANSWER THE QUESTION
If a constant is added to each value in a given data set to produce a new data set, which one of the following describes how the standard deviation of the new data compares to the standard deviation of the original data set? A. Larger B. Smaller C. Equal to
Answer: C. Equal to
Step-by-step explanation:
The standard deviation is written as:
Sx = √( ∑(xₙ - x)^2/(n-1))
Where xₙ are the values of the data set, n is the number of data points and x is the mean of the data set.
Now, if we add a constant c to all the terms in our data set we will have:
(i will use the ' to denote the transformed data)
xₙ' are now xₙ + c.
And the new mean will be:
x' = ( (x₁ + c) + (x₂ + c) + .... + (xₙ + c))/n = (c*n + (x₁ + x₂ + ..))/n = c + (x₁ + x₂ +...)/n
x' = c + x
Then the new standard deviation will be:
Sx' =√( ∑(xₙ' - x')^2/(n-1))
Sx' = √( ∑((xₙ+c) - (x +c))^2/(n-1)) = √( ∑(xₙ - x)^2/(n-1)) = Sx
So the standard deviation does not change.
The correct option is C.
Select the correct text in the table. Use the fundamental theorem of algebra to determine whether each statement is sometimes true, always true, or never true.
1. A quadratic function has 2 distinct roots. always sometimes never
2. A cubic function has at least 1 real root. always sometimes never
3. A function with a degree of 5 has 5 roots. always sometimes never
4. A quadratic function can have only 1 complex solution. always sometimes never
Answer:
1. Sometimes
2. Sometimes
3. Always
4. Sometimes
Step-by-step explanation:
1. Quadratic function : in which maximum power of \(x\) is two.
The roots of quadratic function can be either equal or different.
For example:
\(x^{2} -2x+1\) will have two equal roots i.e. 1 and 1.\(x^{2} -3x+2\) will have two different roots i.e. 1 and 2.So, sometimes is the correct answer.
2. Cubic function has atleast 1 real root.
Cubic function has maximum power of \(x\) as 3.
If the coefficients are real numbers then atleast 1 real root.
If the coefficients are imaginary in nature, then this is not true.
For example:
Cubic equation \(x^3 +i = 0\) does not have any real root.
Cubic equation \(x^3 +1 = 0\) has a real root x = -1.
So, it is sometimes true.
3. A function with degree 5 i.e. maximum power of \(x\) as 5 will have 5 roots.
It is always true that a function will have number of roots equal to its degree.
4. Quadratic function can have only 1 complex solution.
Two complex solutions are also possible for a quadratic function.
For example:
\(x^{2} +1=0\) will have two imaginary roots: \(x=i, -i\)
It is also possible to have 1 complex solution,
For example:
\((x-1)(x-i) = 0\) will have one complex root and one real root.
So, the statement is sometimes true.
Answer:
MY ANSWER IS CORRECT IN PLATO!!!
1. Sometimes
2. Always
3. Always
4. Never
Step-by-step explanation:
1. A quadratic function has 2 distinct roots SOMETIMES
2. A cubic Function has at least 1 root ALWAYS
3. A function with a degree of 5 has 5 roots ALWAYS
4. A quadratic function can have only 1 complex solution NEVER
I JUST GOT 100% on the quiz in PLATO
Select all the rates that are unit rates.
1/1/3
2/3/1
2/3
3/1
1/9
help due today
ill give brainliest and 5 stars
Answer:
3/1
Step-by-step explanation:
All unit rates have a denominator of 1.
ABC~A'B'C'. Their scale factor is 7:9. If the perimeter of smaller ABC is 42, then the
perimeter of A'B'C' is.
Pls hurry!!
Answer:
54
Step-by-step explanation:
ratio is 7:9
7=42
9=?
9×42÷7
Please awnser asap I will brainlist
The element of A n B is { 7, 8}
What is set?A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind.
For example, if the element of P is even numbers from 1 to 20 and element of Q is factor of 6 from 1 to 20 then we can say that set Q is a subset of set P.
The sign 'n' means intersection and this means what is common to two or more set.
If set A = { 1,2,5,7,8}
set B = { 6,7,8,9}
then we can see that 7 and 8 are common to both sides, then
A n B = { 7,8}
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100 Points! Algebra question. Photo attached. State the amplitude, period, and phase shift for the function. Then graph the function. Please show as much work as possible. Thank you!
1. The amplitude is 1
2. The period is 2π
3. The phase shift is 90
4. The vertical shift is 0
5. The graph is attached
How to determine the amplitude and period of the functionFrom the question, we have the following parameters that can be used in our computation:
y = sin[θ + 90)
A sinusoidal function is represented as
f(x) = Asin(B(x + C)) + D
Where
Amplitude = APeriod = 2π/BPhase shift = CVertical shift = DSo, we have
Amplitude = 1
Period = 2π/1
Phase shift = 90
Vertical shift = 0
Evaluate
Amplitude = 1
Period = 2π
Phase shift = 90
Vertical shift = 0
Hence, the amplitude is 1 and the period is 2π
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