One-to-One Functions. ... If no horizontal line intersects the graph of the function f in more than one point, then the function is 1 -to- 1 . A function f has an inverse f−1 (read f inverse) if and only if the function is 1 -to- 1 .
Elizabeth lives in San Francisco and works in Mountain View. In the morning, she has 3 transportation options (take a bus, a cab, or a train) to work, and in the evening she has the same 3 choices for her trip home.
If Elizabeth randomly chooses her ride in the morning and in the evening, what is the probability that she'll use a cab exactly one time?
Answer:
4/9
Step-by-step explanation:
The possibilities of transportation: (The first will be for morning, second will be for afternoon)
B, B
B, C
B, T
C, B
C, C
C, T
T, B
T, C
T, T
It is clearly seen that there are 9 transportation options.
(Using cab 1 time we have BC, CB, CT, TC. So four of the transportation methods use cab one time.)
Therefore, the probability that she will use a cab only once is 4/9.
Line segment OC splits AOB into two angles. Find AOC, if AOB = 155 degree, and m COB is 15 degrees less than m AOC.
Answer:
Step-by-step explanation:
The diagram representing the scenario is shown in the attached photo. From the photo, lines AO, BO and CO meet at a common point O. Since angle AOB is 155 degrees and angle COB is 15 degrees lesser, then angle COB is
155 - 15 = 140 degrees
Recall, the sum of the angles at a point is 360 degrees. Therefore, the sum of the angles at point O is
Angle AOC + 140 + 155 = 360
Angle AOC + 295 = 360
Angle AOC = 360 - 295 = 65 degrees
Which number line represents the solution set for the inequality 2x - 62 6(x - 2) + 8?
-15
-0.5
0
0.5
1
1.5
-1.5
-1
-0.5
0
0.5
1.5
-1.5
-1
-0.5
0
0.5
1.5
-1.5
-1.5
0
0.5
1
1.5
Answer:
2x - 6 ≥ 6(x-2) + 8
2x - 6 ≥ 6x - 12 + 8
6x - 2x ≤ - 6 + 4
4x ≤ -2
4x/4 ≤ -2/4
x ≤ -1/2
Interval Notation: (- ∞, -1/2]
The line starts from -1/2 with the arrow going to the left (decreasing). The endpoint or value from where it started, which is -1/2, should be shaded. The inequality symbol x ≤ -1/2 represents the values at most or maximum -1/2.
Step-by-step explanation:
The number line representing the solution set for the inequality given is option C.
The inequality is 2x - 6 ≥ 6(x-2) + 8,
Solving for x,
2x - 6 ≥ 6(x-2) + 8
2x - 6 ≥ 6x - 12 + 8
6x - 2x ≤ - 6 + 4
4x ≤ -2
4x/4 ≤ -2/4
x ≤ -1/2
Therefore, the Interval Notation is (- ∞, -1/2]
This means that the all the values of x will be less than -1/2 or equal to it,
Therefore, the graph will be, the line starts from -1/2 with the arrow going to the left (decreasing).
Learn more about inequality, click;
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Which pairs of angles in the figure below are vertical angles?
Step-by-step explanation:
Vertical angles are opposite angles formed by two intersecting lines.
The only lines that fully intersect are TSI and WSN.
Now find the opposite angles that are formed by the lines TSI and WSN.
Answer:
TSN ISW and ISN and TSW
Step-by-step explanation:
Find all possible values of the fraction below. (Assume different letters are different digits, and the same letters are the same digits.)
Answer:
{0, undefined}
Step-by-step explanation:
There are 10 unique letters in the expression, so each one must stand for a different digit. Assuming the digits are multiplied as indicated, the digit 0 must appear in either the numerator or the denominator.
If 0 appears in the numerator, the value of the fraction is 0.
If 0 appears in the denominator, the value of the fraction is "undefined."
The only possible values of this fraction are {0, undefined}.
Michael just drank a cup of coffee to help him stay awake. The coffee had 110 milligrams of caffeine in it. If his body
processes 5% of the caffeine every hour, how much will be left in 8 hours?
The body uses 5%, so 95% of the previous amount is left every hour:
Total = start value x (1- %)^time
Total = 110 x(0.95)^8
Total left = 72.9762 milligrams
Round the answer as needed.
£620 is divided between Malachy, Paul & Brian so that Malachy gets twice as much as Paul, and Paul gets three times as much as Brian. How much does Paul get?
Answer: Paul gets £186
Step-by-step explanation:
Paul has 1/2 as much as Malachy, and Brian has 1/3 as much Paul, therefore Brian has 1/6 as much as Malachy.
1/2 * 1/3 = 1/6
So Malachy’s amount equals 1 in this equation, Paul’s amount equals 1/2 in this equation, and Brian’s amount equals 1/6 in this equation.
1 + 1/2 + 1/6 = 1 + 3/6 + 1/6 = 1 4/6
Now, divide 620 by 1 4/6 to find Malachy’s amount.
620/1 4/6 = 372
Now, divde 372 by 2 to get Paul’s amount.
372/2 = 186
On a coordinate plane, a parabola opens up in quadrant 1. It goes through (2, 12), has a vertex at (5, 3), and goes through (8, 12). Write the equation of the function whose graph is shown. y = (x + )2 +.
Answer:
Step-by-step explanation:
You have a vertex coordinate and 2 points. In order to write the equation for that parabola, you only need the vertex and one point. We will fill in the following work form of the parabola:
[tex]y=a(x-h)^2+k[/tex] , where h and k are from the vertex and x and y are from the point. Filling in:
[tex]12=a(8-5)^2+3[/tex] and
[tex]12=a(3)^2+3[/tex] and
[tex]12=9a+3[/tex] and
9 = 9a s0
a = 1.
Now we can write the equation, filling in a, the only unknown we had, which we now know is 1:
[tex]y=1(x-5)^2+3[/tex]
Answer:
y = 1 (x + -5 )2 + 3
Step-by-step explanation:
Please help I’m really struggling with this
Answer:
[tex]y=\frac{1}{3} x+4[/tex]
Step-by-step explanation:
A linear equation is written as [tex]y=mx+b[/tex], "m" being the slope and "b" being the y-intercept.
The slope is how many times you rise/run in order to get from one point on the line to the next. You rise (go up/down) 1 unit and run (go left/right) 3 units. Plug in the numbers and you get 1/3.
The y-intercept is where the graph lands on the y-axis, which is 4.
y = 1/3x + 4
Step-by-step explanation:
y = ax + b
b = the intercept with the y-as.
In the graph, the linear function (which is a fancy word for a line), you can see that the incline with the y-axis is at point (0,4).
So, b = 4
a = slope or incline.
To easilly find "a", you can follow these steps:
1. You choose two "nice" poins.
2. Starting on one point of the line, you count how many units you need to go in horizontal direction and in vertical direction to end upon the another point on the line.
3. The fraction a = y units/x units
1. Choose two nice point
Starting from (0,4) and going to the next "nice" point for example (3, 5).
2. Horizontal 3 units to the right, and 1 unit up.
3. a = y units/x units
a = 1/3
y = 1/3x + 4
I need help please help me
Answer:
SSS
Step-by-step explanation:
ST = YA, SY = TA Given
AS = SA Reflexive property
ΔSTA ≅ ΔAYS SSS
3 x 4 x 5 x m x n = ???????
what does it equal???
The equivalent expression for the given expression is 60mn.
The given expression is 3×4×5×m×n.
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
Here, 3×4×5×m×n = 60mn
Therefore, the equivalent expression for the given expression is 60mn.
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The measure of one angle of a triangle is 105°. What do you know about the measures of the other two angles? Check all that apply.
Both angles are acute.
The sum of the measures of the two angles is 75°.
The sum of the measures of the two angles is 155°.
One of the angles is a right angle.
The measure of neither angle is more than 75°.
The measures of the other angles must be 105° too.
The measure of one of the other angles equals 75°.
The measure of one of the other angles must be 45°.
Step-by-step explanation:
The sum of the measures of the two angles is 75° because of the sum of angles in a triangle which means that both angles are acute. This also means that the measure of neither angle is more than 75°.
Answer:
A, B, E
Step-by-step explanation:
both angles are acute
The sum of the measures of the two angles is 75°
The measure of neither angle is more than 75°
The weight of a honeybee is 1.2\cdot10^{-1}\text{ g}1.2⋅10 −1 g1, point, 2, dot, 10, start superscript, minus, 1, end superscript, start text, space, g, end text. The weight of the pollen collected by the bee on one trip is 6.0 \cdot 10^{-2} \text{ g}6.0⋅10 −2 g6, point, 0, dot, 10, start superscript, minus, 2, end superscript, start text, space, g, end text.
Answer:1.8*10^-1
Step-by-step explanation:
Answer: 1.8 x 10^−1
Step-by-step explanation:
Help pls :/.
The net of a triangular prism and its dimensions are shown. What is the total surface area, in square inches, of the triangular prism?
A) 240 sq inches
B) 120 sq inches
C) 96 sq inches
D) 24 sq inches
Answer:
120 sq inches
Step-by-step explanation:
I just did the quiz just now
Part 3. Find the measure of the indicated angle to the nearest degree.
Answer:
hope this helps you
What is the unit price for an ounce of coffee if a 120-ounce package costs $9.60?
answers
_______________________________
Hey!!
Solution,
cost of 120 ounce of coffee= $9.60
cost of an ounce of coffee= 9.60/120
=$ 0.08
Hope it helps
Good luck on your assignment
_____________________________
Answer:
So for an estimation my answer would be 0.08
Step-by-step explanation:
Do 9.60 divided by 120.
Hope this helps, have a good day! :)
(Picture of formula and work below)
Meredith has two different-sized bags of trail mix. The larger bag contains 6.18 ounces of trail mix. The smaller bag contains 6.8 ounces of trail mix. Which bag contains more trail mix? Why?
Answer:
The smaller bag
Step-by-step explanation:
The smaller bag contains more trail mix.
This is because the quantity of trail mix in the smaller bag (6.8 ounces) is more than that in the larger bag (6.18 ounces).
This makes sense because we are not told the capacities of the bags, so, it is possible that both bags are able to contain much more than 6.8 ounces.
PLEASE HELP WILL MARK BRAINLIEST
How would the rotational speed of the anemometer be different during a strong windstorm than in a wind that is not as strong?
Answer: the rotational speed would be greater during a storm
Step-by-step explanation:
Rotational speed is produced by a torque on an object relative to a pivot. The stronger the wind, the stronger the torque on the anemometer. This increase in net torque would increase the angular acceleration of the anemometer, which would increase the angular velocity (rotational speed).
Jada is solving the equation shown below.
Negative one-half (x + 4) = 6
Which is a possible first step to begin to simplify the equation? Select two options.
Divide both sides of the equation by –2.
Subtract 4 from both sides of the equation.
Multiply both sides of the equation by –2.
Distribute –2 over (x + 4).
Distribute Negative one-half over (x + 4).
Answer:
Distribute -1/2 over (x - 4)
Divide both sides of the equation by -2
The first step to begin to simplify the equation is to multiply both sides of the equation by -2
To find the first step to simplify the equation.
Given:The given equation
=-1/2(x + 4) = 6
Simplification:First, we will multiply both sides of the equation by -2
we get,
x + 4 = -12
x = -12-4 = -16
Hence, the value of x is -16.
Therefore, the first step is to multiply both sides of the equation by -2.
To learn how to find the first step to simplify the equation, refer:
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Please help! Correct answer only please! I need to finish this assignment by today.
Doug is birdwatching at the coast. He records each bird he sees.
What is the experimental probability that the next bird Doug sees will be a cormorant?
Simplify your answer and write it as a fraction or whole number.
Answer:
1/2
Step-by-step explanation:
During his time bird watching, he sees 1+1+5+8+1=16 different birds in total. Out of those, 8 are cormorant, which means that the experimental probability that the next one is is 8/16=1/2. Hope this helps!
(check the pic) please help asp!! 37 points for this and if you answer this fully I will make you brainilest!
Answer:
See explanation
Step-by-step explanation:
During September, they ran half a mile once, 1 mile twice, 1.5 miles 4 times, and 1.75 miles once. This is a total of 8 runs below 2 miles in length. Meanwhile, they ran 2 miles twice, 2.5 miles twice, 2.75 miles 4 times, and 3 miles 5 times, a total of 13 runs over 2 miles. Therefore, Michelle is correct. Hope this helps!
Which of the following is a correct representation of the polynomial F(x)=x^4-5x^2+4 as a product of linear factors
Answer:
C
Step-by-step explanation:
how to find the correct one?
just see on the x² constant number. it's -5 so
from ABCD the only option give -5 is C
A. (-2)(-2) + (-1)(-1) = 5
B. (-2)(-2) + (1)(1) = 5
C. (2)(-2) + (-1)(1) = -5
D. (-2)(2) + (-1)(-1) = -3
which 3 sticks should he use (there’s a picture of the problem)
Answer:
The answer is number three
Step-by-step explanation:
I know this because the formula for pythageon theorm is. (A)squared + (B)squared = (C)squared so if you substitude the value of number three into the therom it would be equal to this 6x6+8x8=10x10
then if you simplify it would equal 36 + 64 = 100 and so this would satisfy the therom.
Plzzzz help fast !!
One month Chris Rented 3 movies and 2 video games for a total of $15 . the next month he rented 8 movies and 4 video games for a total of $33. find the rental cost for each movie and each video game
Answer:
Both are a total of $3
Step-by-step explanation:
Because if you add 3+2= 5 and then you divided; 15÷5= 3, then you add 8+4=12, and you do the same like the other; 33÷12= 2.75 and if you round it, the answer will be 3.
So in conclusion both the movies and the video games are $3
If 2> -a, then a < -2.
True
False
Answer:
False
Step-by-step explanation:
Flip the equation.
−a<2
Divide both sides by -1.
a>−2
What is the range of the function f(x) = |x − 1| − 2? All real numbers all real numbers less than or equal to −2 all real numbers less than or equal to 1 all real numbers greater than or equal to −2
Answer:
B.)
Step-by-step explanation:
Took test
Expand and Simplify (x+7)(x+5)
Answer:
[tex]=x^2+12x+35[/tex]
Step-by-step explanation:
[tex]\left(x+7\right)\left(x+5\right)[/tex]
[tex]\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd[/tex]
[tex]a=x,\:b=7,\:c=x,\:d=5\\=xx+x\cdot \:5+7x+7\cdot \:5\\=xx+5x+7x+7\cdot \:5\\=x^2+12x+35[/tex]
The volume of a rectangular prism can be found by multiplying the base area, B, times the height. If the volume of the prism is represented by 15x2 + x + 2 and the height is x2, which expression represents B, the area of the base? 15x + + 15x + + 15 + + 15 + +
Answer:
[tex]Base (B) = /frac{15x² + 1 + 2}{x}[/tex]
Step-by-step Explanation:
==>Given:
Dimensions of a rectangular prism are expressed as follow:
Volume (V) = 15x² + x + 2
Height (h) = x²
==>Required:
Expression of the Base area (B)
==>Solution:
Volume (V) = Base (B) × Height (h)
15x² + x + 2 = B × x²
Divide both sides by x²
[tex]\frac{15x² + x + 2}{x²} = B
[tex]Base (B) = /frac{15x² + 1 + 2}{x}[/tex]
Answer: c
Step-by-step explanation:
(algebra) i think of a number add 3 to it and multiply the result by seven what is the answer
Answer:
[tex]7x+21[/tex]
Step-by-step explanation:
Let the number be [tex]x[/tex].
[tex]x+3[/tex]
[tex]7(x+3)[/tex]
Expand the brackets.
[tex]7x+21[/tex]
If trapezoid JKLM is translated according to the rule (x,y)—> (x+2, y - 6), what are the coordinates of point L
Answer:
( x, y) is translation '2' units right and '6' units down
(x ,y))—> (x +2 ,y-6)
Step-by-step explanation:
Explanation:-
Type of transformation change to co-ordinate point
vertical translation up 'd' units (x,y) changes to (x , y+d)
vertical translation down 'd' units (x,y) changes to (x , y-d)
Horizontal translation left 'c' units (x,y) changes to (x-c , y)
Horizontal translation right 'c' units (x,y) changes to (x+c , y)
Now by use above table
given data ( x, y) is translation '2' units right and '6' units down
(x ,y))—> (x +2 ,y-6)
Final answer:-
( x, y) is translation '2' units right and '6' units down
(x ,y))—> (x +2 ,y-6)
