Answers
x^2+3x-10
(x+5)(x-2)
(x-2)/((x+5)(x-2))
The x-2 in the numerator and denominator cancel out.
Final answer: x+5
Related Questions
For one week at your store, employees worked 200 regular hours and 50 hours of overtime. what percent of the total hours for the week were overtime?
Answers
total hours = 200+50 = 250
50 were overtime
50/250=0.20 = 20% of the hours were overtime
The waiting times between a subway departure schedule and the arrival of a passenger are uniformly distributed between 00 and 66 minutes. find the probability that a randomly selected passenger has a waiting time greater thangreater than 3.253.25 minutes. find the probability that a randomly selected passenger has a waiting time greater thangreater than 3.253.25 minutes.
Answers
Le us denote P as the probability that the randomly selected passenger has a waiting time greater than 3.25 minutes.
P = (length of the shaded region) x (height of the shaded region)
P = (6 - 3.25) * (0.167)
P = 2.75 * 0.167
P = 0.40915
P = 0.41
Each week Rosario drive to an ice-skating rink that is 60 miles away. The road trip takes 2.75 hours. If he averages 55 mph on his way to the rink, which equation can be used to find X, the number of miles per hour he averages on his way home?
Answers
Answer: The number of miles per hour he averages on his way home is 36 mph.
Step-by-step explanation:
Since we have given that
Distance traveled by Rosario = 60 miles
Time taken for road trip = 2.75 hours
Speed at which he on his way to the rink = 55 mph
Let X be the speed at which he averages on his way home.
So, According to question, we get that,
[tex]\dfrac{60}{55}+\dfrac{60}{x}=2.75\\\\1.09+\dfrac{60}{x}=2.75\\\\\dfrac{60}{x}=2.75-1.09\\\\\dfrac{60}{x}=1.659\\\\x=\dfrac{60}{1.659}\\\\x=36.16\\\\x=36\ mph[/tex]
Hence, the number of miles per hour he averages on his way home is 36 mph.
Which double-angle or half-angle identity would you use to verify that 1+cos2a=2/1+tan2a?
Answers
In this case or scenario,
the double-angle identity that should be used is the one for cosine.
In totality, we shall need the following three trigonometric
identities to end up with the equality:
1. cos (2a) = cos² (a) - sin² (a)
2. sin² (a) + cos² (a) = 1
3. tan² (a) + 1 = sec²
(a)
Using identities 1 and 2 on the left-hand side of the
equation, we get the following:
1 + cos (2a) = 1 + cos² (a) - sin² (a) = 2 cos² (a)
Recalling that cos² (a) = 1 / sec² (a) and applying identity
3, we find the following:
2 cos² (a) = 2 / sec² (a) = 2 / (1 + tan² (a))
Therefore giving us:
2 cos² (a) = 2 / (1 + tan² (a))
Answer:
Its C. cos2a=cos^2a-sin^2a on ed
Find the exact value of cos 75 by using a sum or difference formula
Answers
Formula: cos 45 x cos 30 - sin 45 x sin 30
Cos 45 = root 2 / 2
Cos 30 = root 3 / 2
Sin 45 = root 2 / 2
Sin 30 = 1 / 2
The exact value of cos 75 is (√6 - √2)/4 or 0.2588190.
What is Trigonometry?Trigonometry is a discipline of mathematics that studies the relationship between the sides of a triangle (right triangle) and their angles. There are six trigonometric functions that define the relationship between sides and angles.
We have to find the exact value of cos 75.
So, The value of cos 75 degrees in decimal is 0.258819045.
Then,
cos 75°
= cos (1.3089)
= (√6 - √2)/4 or 0.2588190
Learn more about Trigonometry here:
https://brainly.com/question/29002217
#SPJ7
Two sides of a triangle are 6 m and 10 m in length and the angle between them is increasing at a rate of 0.06 rad/s. find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is π 3 rad.
Answers
Final answer:
To find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is π/3 rad, we need to differentiate the formula for the area of a triangle with respect to time.
Explanation:
Rate of Change of Triangle Area with Increasing Angle
To find the rate at which the area of the triangle is increasing, we need to differentiate the formula for the area of a triangle with respect to time.
The formula for the area of a triangle is given by: A = 0.5 × a × b × sin(C), where a and b are the lengths of the two sides and C is the angle between them.
By differentiating this formula with respect to time, we can find the rate of change of the area with respect to time.
When the angle between the sides is π/3 rad, substitute the length of the sides and the rate at which the angle is increasing, and solve for the rate of change of area.
A card is picked from a standard deck of 52 cards. determine the odds against and the odds in favor of selecting a 10
Answers
The odds in favor of drawing a '10' from a standard 52-card deck are 1 to 12, and the odds against are 12 to 1.
Explanation:In a standard deck of 52 cards, there are four '10' cards - one each of hearts, diamonds, clubs, and spades. Hence the probability of drawing a '10' is 4 out of 52, or simplified, 1 out of 13.
Therefore, the odds in favor of selecting a '10' (i.e., the probability of selecting a '10' versus not selecting a '10') are 1 to 12 because for each '10' card there are 12 others that are not '10s'.
The odds against selecting a '10' are simply the inverse of the odds in favor. That is, for every one time you may draw a '10', there are 12 other times when you would draw something else, hence the odds against drawing a '10' are 12 to 1.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ3
Alan bought a suit on sale for $558. This price was 28% less than the original price. What was the original price?
Answers
divide both sides by 0.72=775
the original price was $775
What is 7.75×10-1 in standard notation
Answers
Note that 10⁻¹ = 1/10 = 0.1
7.75 x 0.1 = 0.775
If five cakes cost 5 pounds how much do 2 cakes cost
Answers
You have five cakes, and it costs 5 pounds. What is the price of each cake?
Well.. It has to be 1! So, if you have two cakes - it will cost 2 pounds. Wanna go extra and get 30 cakes? 30 pounds!
Please help! Geometry.
Answers
[tex]sin(51)= \frac{y}{12} [/tex]
and 12 sin(51) = y and y = 9.325
The second one has the reference angle as the unknown. You could use any of the identities here because you have all the sides of the triangle, but I will use sin again:
[tex]sin \beta = \frac{12}{13} [/tex]
and [tex]sin \beta =.9230769[/tex]
and [tex]sin ^{-1}(.9230769)=67.38 [/tex]
The next one has a referece angle of 13 with 24 being the side adjacent to it and the unknown being the side across from it. You will use the tangent identity here:
[tex]tan(13)= \frac{x}{24} [/tex]
and 24 tan(13) = x so x = 5.540
The last one has a reference angle of 20 with the hypotenuse as the unknown x, and the side across from it as 10. Use the sin identity again:
[tex]sin(20)= \frac{10}{x} [/tex] and
[tex]x sin(20)=10 [/tex] and
[tex]x= \frac{10}{sin(20)} [/tex] with x = 29.238
Everything is in regards to the reference angle; you HAVE to be able to identify the reference angle and then how the given sides are related to it.
the _____ of a central angle are two radii of the circle.
A. sides
B. arcs
C. verticals
D. measures
Answers
A.sides
Answer:
A.Sides.
Step-by-step explanation:
The central angle is the angle made by any arc at the center of the circle.Central angle is formed by two rays from the centre which cuts the circle at two points .The part of the two rays which lie inside the circle is the radius of the circle .
We say :
The sides of a central angle are two radii of the circle.
Help plzzzzz!!!!!!!!!!
Answers
1. less than or equal to 5
2. greater than 5
3. less than 5
Use the remainder theorem to determine the remainder when 3t2 + 5t − 7 is divided by t − 5. A. 93 B. 43 C. 107 D. 57
Answers
[tex]P(t) = 3t^{2} + 5t - 7[/tex]
Substitute t = 5 into the equation:
[tex]P(5) = 3(5)^{2} + 5^{2} - 7[/tex]
[tex]P(5) = 75 + 25 - 7 = 93[/tex]
Thus, we get a remainder of 93 or (A)
Find the sum of a finite arithmetic sequence from n = 1 to n = 13, using the expression 3n + 3.
Answers
So the first term is 3+3 and the last term is 3(13)+3
So the sum is:
13(6+42)/2
312
Answer:
The sum of a finite arithmetic sequence from n = 1 to n = 13 is 312.
Step-by-step explanation:
The given expression is
[tex]3n+3[/tex]
For n=1,
[tex]3(1)+3=6[/tex]
For n=2,
[tex]3(2)+3=9[/tex]
For n=3,
[tex]3(3)+3=12[/tex]
The required AP is
[tex]6, 9, 12, ...[/tex]
Here first term is 6 and common difference is 3.
The sum of n terms of an AP is
[tex]S_n=\frac{n}{2}[2a+(n-1)d][/tex]
[tex]S_{13}=\frac{13}{2}[2(6)+(13-1)(3)][/tex]
[tex]S_{13}=\frac{13}{2}[12+36][/tex]
[tex]S_{13}=312[/tex]
Therefore the sum of a finite arithmetic sequence from n = 1 to n = 13 is 312.
What is the equation of a quadratic graph with a Focus of (8,-8) and directrix of y=-6
Answers
so hmmm the left-side of the picture, is the focus point and the directrix, notice, the directrix is a horizontal line, that means the parabola is a vertically opening one.
also notice, the focus point is below the directrix, that means the parabola opens downwards
now, the vertex is "p" distance from either the directrix and the focus point, so that means, the vertex is half-way between those two fellows, if you notice the right-side of the picture, that's where the vertex is at.
the distance "p" is clearly just 1unit, however, since the parabola is opening downwards, "p" is negative, thus -1
[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} (y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\ \boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}}) }\\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\[/tex]
[tex]\bf \begin{cases} h=8\\ k=-7\\ p=-1 \end{cases}\implies (x-8)^2=4(-1)(y-(-7)) \\\\\\ (x-8)^2=-4(y+7)\implies \cfrac{(x-8)^2}{-4}=y+7 \\\\\\ -\cfrac{1}{4}(x-8)^2-7=y[/tex]
Which method(s) can be used to solve a system of equations? Select all that apply.
distributing
graphing
substitution
formulas
addition
modeling
Answers
Answer:graphong, substitution, addition
Step-by-step explanation:
A point is on a circle if the distance from the center of the circle to the point is equal to the
a) area.
b)circumference.
c)radius.
d)diameter.
Answers
The distance from the centre of the circle to any point on the circumference of the circle is called the radius.
The original price P of an item less a discount of 20% ?
Answers
P(0.80)
Answer:
0.8 P
Step-by-step explanation:
Let the origional price of P
A discount of 20% is given on the item
The price of item=[P(100-d)]÷100
The price of the item= [tex]\frac{p(100-20)}{100}[/tex]
The price of the item= [tex]\frac{p(80)}{100}[/tex]
The price of the item= 0.8 P
If the discount 20% is given on origional price of the item, than the price will be 0.8 P
Hence, the correct answer is 0.8 P
Determine the quadrant when the terminal side of the angle lies according to the following conditions: cos(t)>0, tan(t)>0
Answers
tan(angle) = sin(angle)/cos(angle), so it's a division. sin(angle) has the sign of the y axis.
So, tan(t)>0, mus be +/+ or -/-, quadrant I or III, respectively.
The only in common is quadrant I. Hope it helps for the next one!
Amy wants to buy a pair of jeans that cost $65. Today the store is offering a straight discount of 25%. Calculate her savings and cost after the discount.
Answers
[tex]\bf \begin{array}{ccllll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 65&100\\ x&25 \end{array}\implies \cfrac{65}{x}=\cfrac{100}{25}[/tex]
solve for "x", that's her savings
the cost of the jeans is 65 - x
Answer:
Amy's discount is $16.25, and the cost after the discount is $48.75.
Step-by-step explanation:
The risk set by the researcher for rejecting a null hypothesis when it is true is called the
Answers
_____________________________
Mount Rushmore is a sculpture that was carved using a model with a scale of 1 in :1 ft. If the model of George Washington’s face was 5 ft tall, how tall is his face on Mount Rushmore?
Answers
The height of the face is 60 inch.
What is unit conversion?Unit conversion is a multi-step process that involves multiplication or division by a numerical factor, selection of the correct number of significant digits, and rounding.
As 1inch = 1ft,
then to find out how many inches is George Washington’s face.
As there are 12inch in a foot
=12*5
=60inches
Thus , his face is 60ft tall.
Learn more about unit conversion here:
https://brainly.com/question/13899873
#SPJ2
PLEASE HELP!!!! IMAGE ATTACHED FIND THE MEASURE OF ANGLE 3
Answers
m< 3 = 30
answer
30
I need help and I'm not sure if the answer is A so can you pls help!
Answers
The answer is D because -5 is less than 1 and its not equal to 1.
In a community fitness group, 40% of members run for exercise and 36% of members run and play a sport. What percentage of members who run for exercise also play a sport?
Answers
By dividing the percentage of community fitness group members who run and play a sport (36%) by those who run for exercise (40%), we find that 90% of the members who run for exercise also play a sport.
To determine the percentage of community fitness group members who run for exercise and also play a sport, we can use the information provided. The question states that 40% of members run for exercise and 36% of members run and play a sport. To find what percentage of members who run also play a sport, we need to find the proportion of runners who are also sport players.
To do this, we divide the percentage of members who run and play a sport by the percentage who only run:
Percentage of runners who also play a sport = (Percentage of members who run and play a sport) / (Percentage of members who run for exercise)
So,
Percentage of runners who also play a sport = 36% / 40% = 0.9
We then multiply by 100 to convert this to a percentage:
0.9 × 100 = 90%.
Therefore, 90% of the members who run for exercise also play a sport.
The size of angle aob is equal to 132 degrees and the size of angle cod is equal to 141 degrees. find the size of angle dob.
Answers
angle AOB = 132 and is also the sum of angles AOD and
DOB. Hence
angle AOD + angle DOB = 132° ---> 1
angle COD = 141 and is also the sum of angles COB and BOD. Hence
angle COB + angle DOB = 141° ---> 2
Now we add the left sides together and the right sides of equations 1 and 2
together to form a new equation.
angle AOD + angle DOB + angle COB + angle DOB = 132 + 141 ---> 3
We should also note that:
angle AOD + angle DOB + angle COB = 180°
Therefore substituting angle AOD + angle DOB + angle COB in equation 3 by 180
and solving for angle DOB:
180 + angle DOB = 132 + 141
angle DOB = 273 - 180 = 93°
Find the solution of this system of equations.
Separate the x- and y-values with a comma.
x= 12 + y
18x – 12y= 18
Answers
18x – 12y= 18
substitute x= 12 + y into 18x – 12y= 18
18x – 12y= 18
18(12 + y) – 12y= 18
36 + 18y - 12y = 18
6y =-18
y = -3
x= 12 + y
x= 12 -3
x = 9
solution (9, -3)
18(12+y)-12y=18 perform indicated multiplication on left side
216+18y-12y=18 combine like terms on left side
216+6y=18 subtract 216 from both sides
6y=-198 divide both sides by 6
y=-33, which makes x=12+y become:
x=12-33
x=-21
So the solution to this system of equations is the point (-21, -33)
19. You roll two standard number cubes. What is the probability that the sum is odd, given than one of the number cubes shows a 1? Show your work.
Answers
6 numbers per cube
if one is a 1, then the other one has to be a 2, 4 or 6 to be an odd sum
1+2=3, 1+4=5,1+6=7
since there are 3 numbers you can get that would be a 3/6 ( reduce to 1/2) probability
so 1/2 probability
1/2 is wrong, I put it on my exam and got it wrong:/
What is a tangent of a circle