Answer:
1. h(x) = x + 5—> f(x) = x² + 4x - 5, and g(x) = x - 1
2. h(x) = x + 3 —> f(x) = x² - 9, and g(x) = x - 3
3. h(x) = x + 4—> f(x) = x² - 16, and g(x) = x - 4
4.h(x) = x - 1—> f(x) = x² - 4x + 3, and g(x)= x - 3
Step-by-step explanation:
A) f(x) = x² - 9, and g(x) = x - 3
We are told that; h(x) = f(x)/g(x)
f(x) = x² - 9 can be factorized to;
f(x) = (x + 3)(x - 3)
Thus; h(x) = (x + 3)(x - 3)/(x - 3)
(x - 3) will cancel out to give;
h(x) = x + 3
B) f(x) = x² - 4x + 3, and g(x)= x - 3
x² - 4x + 3 can be factorized as;
(x - 1)(x - 3)
Thus; f(x) = (x - 1)(x - 3)
h(x) = (x - 1)(x - 3)/(x - 3)
h(x) = x - 1
C) f(x) = x² + 4x - 5, and g(x) = x - 1
x² + 4x - 5 can be factorized as;
(x - 1)(x + 5)
Thus; f(x) = (x - 1)(x + 5)
h(x) = (x - 1)(x + 5)/(x - 1)
h(x) = x + 5
D) f(x) = x² - 16, and g(x) = x - 4
x² - 16 can be expressed as;
(x + 4)(x - 4)
Thus; f(x) = (x + 4)(x - 4)
h(x) = (x + 4)(x - 4)/(x - 4)
h(x) = x + 4
what solutions to the following quadratic
3x^2 +15x-18=0
Answer:
x=-6 and x=1
Step-by-step explanation:
Given that:
[tex]3x^2+15x-18[/tex]
Now,
[tex]3x^2+15x-18=0\\[/tex]
Using the quadratic formula where a=3, b=15, and C=-18
x=-b±[tex]\sqrt{b^2-4ac} /2a[/tex]
x=-15±[tex]{\sqrt{15^2-4(3)(-18} } /2(3)[/tex]
x=-15±[tex]\sqrt{441} /6[/tex]
the discriminant [tex]b^2-4ac>0[/tex]
So, there are two real roots
x=-15±21/6
[tex]x=\frac{6}{6} \\x=1\\x=\frac{-36}{6} \\x=-6[/tex]
Therefore, x=-6 and x=1
What is the original price of an item cost if the tax is 9.25% and the discount is 25% and the new price after discount and tax is $62.28?
Answer: $ 91.50.
Step-by-step explanation:
Let x be the original price.
Since discount is applied before tax.
New price = (Original price - Discount)-Tax rate (Original price - Discount)
, where Discount = Discount rate x Original price.
Substituting values, we get
[tex]62.28=(x-0.25x)-0.0925(x-0.25x)[/tex]
[tex]62.28=(0.75x)-0.0925(0.75x)[/tex]
[tex]62.28=0.75x-0.069375x[/tex]
[tex]62.28=0.680625x[/tex]
[tex]x=\frac{62.28}{0.680625}[/tex]
[tex]x=91.50[/tex]
Hence, the original price was $ 91.50.
If I had 2 500 apples and sold 200 how much apples would I have left
Answer:
2300 apples
Step-by-step explanation:
2500 - 200 = 2300
Answer:
2300
Step-by-step explanation:
2500 - 200 = 2300
Note: "have left" means the answer after subtraction.
SAT MATH, PLEASE HELP PLEASE THIS IS MY LAST CHANCE
Answer:
[tex] \gamma = 125.00 \: degrees \\ a = 2.18 \\ b = 3.59[/tex]
Step-by-step explanation:
[tex] \gamma = 180 - 20 - 35 \\ = 125 \: degrees[/tex]
[tex]using \: sine \: rule \\ \frac{a}{sin20} = \frac{b}{sin35} = \frac{5.122}{sin125} \\ a = 2.1386 \\ b = 3.5865[/tex]
The graphs of four quadratic equations are shown. Identify the number of real solutions of each equation by
dragging descriptions to each graph.
Answer:
1. 2 real solutions
2. no real solutions
3. 2 real solutions
4. 1 real solution
Step-by-step explanation:
The 'solution' to a quadratic equation means the x - intercepts of a graph, so how many times the parabola crosses the x-axis.
A hiker is standing 40 feet away from a tree that is 50 feet tall.
What is the angle of elevation from the hikers foot to the top of the tree??
HELP ME PLEASE ITS URGENT
Answer:
87.9°
Step-by-step explanation:
arctan(50/40)=87.9°
Five athletes are in a 100k race. How many different ways can they finish based on their order?
Answer:
120 different ways
Step-by-step explanation:
The first person can be 5 different ways
Now there are 4 people left
The second person can be 4 different ways
And so on
5*4*3*2*1
120 different ways
write short note on the rule on how to bisect a perpendicular angle
Answer:
Given a line segment AB
open the compass more than half of the distance between A and B, and scribe arcs of the same radius centered at A and B.
Call the two points where these two arcs meet C and D. Draw the line between C and D.
CD is the perpendicular bisector of the line segment AB. Call the point where CD intersects AB E.
Step-by-step explanation:
for more help please follow
Answer:
Follow the steps below to construct a perpendicular bisector of a line segment.
Step 1: Draw a line segment XY of any suitable length.
Step 2: Take a compass, and with X as the center and with more than half of the line segment XY as width, draw arcs above and below the line segment.
Step 3: Repeat the same step with Y as the center.
Step 4: Label the points of intersection as 'P' and 'Q'.
Step 5: Join the points 'P' and 'Q'. The point at which the perpendicular bisector PQ intersects the line segment XY is its midpoint. Label it as 'O'.
Step-by-step explanation:
If KJ=4 and KM= 2, find ML
Answer:
6
Step-by-step explanation:
(whole secant) * (external part) = (tangent)^2
(KL) * (KM) = KJ^2
(KM+ ML) * KM = KJ^2
(2+ ML) * 2 = 4^2
(2+ ML) * 2 =16
Divide each side by 2
(2+ ML) = 8
Subtract 2 from each side
ML = 6
A researcher selects a sample of participants to test for differences in employment rates among part-time and full-time teachers. Because there are many more women in teaching jobs than men, the researcher selected more women than men for her study to ensure that it represented the actual distribution of men and women teachers in the job sector. Which type of quota sampling was used in this example
Answer: proportionate
Step-by-step explanation:
Proportional quota sampling is when the total number of people that are to be surveyed are decided in advance. This form of sampling is usually used in opinion polls and surveys.
Since due to the fact that there are many more women in teaching jobs than men, the researcher selected more women than men for her study to ensure that it represented the actual distribution of men and women teachers in the job, then this was decided in advance and indicates the proportionate quota sampling.
please help me i have 65 questions i have to do
Today, the population of Canyon Falls is 22{,}50022,50022, comma, 500 and the population of Swift Creek is 15{,}20015,20015, comma, 200. The population of Canyon Falls is decreasing at the rate of 740740740 people each year while the population of Swift Creek is increasing at the rate of 1{,}5001,5001, comma, 500 people each year. Assuming these rates continue into the future, in how many years from today will the population of Swift Creek equal twice the population of Canyon Falls
Answer:
10 years
Step-by-step explanation:
Given :
Population of Canyon falls = 22500
Rate of decrease = 740 per year
Population after x years :
f(x) = 22500 - 740x ; x = number of years
Population of Swift Creek = 15200
Rate of Increase = 1500 per year
Population after x years :
f(x) = 15200 + 1500x ; x = number of years
Number of years when, population of swift creek will be twice that of Canyon falls
15200 + 1500x = 2(22500 - 740x)
15200 + 1500x = 45000 - 1480x
15200 - 45000 = - 1480x - 1500x
-29800 = - 2980x
x = 29800 / 2980
x = 10
After 10 years
The temperature on a thermostat is set to 72∘F, but the actual temperature can vary by as much as 2∘F. Let x represent the actual temperature to create an absolute value inequality to determine the range of possible-actual temperatures.
Any help is much appreciated :)
Using an absolute value inequality, it is found that the range of temperatures is between 70ºF and 74ºF.
---------------
The absolute value function measures the distance of a point to the origin, and is defined by:[tex]|x| = x, x \geq 0[/tex]
[tex]|x| = -x, x < 0[/tex]
---------------
The actual temperature is x, on a thermostat set to 72ºF. It can vary by as much as 2ºF, which means that the absolute value of the difference between x and 72 is at most 2, that is:[tex]|x - 72| \leq 2[/tex]
Solving the inequality:
The term is both greater or equal to -2 and at most 2, thus:[tex]x - 72 \geq >= -2[/tex]
[tex]x \geq 70[/tex]
And
[tex]x - 72 \leq 2[/tex]
[tex]x \leq 74[/tex]
Thus, the range of temperatures is between 70ºF and 74ºF.
A similar problem is given at https://brainly.com/question/24514895
the slope of the line
Answer: -2
Explanation: On the image we can see it goes down 4 units and right 2. Giving us the slope [tex]\frac{-4}{2}[/tex]
Simplified that is -2 which is the slope of the line
At what rate, in minutes per lap, does this swimmer swim?
Answer:
1.6
Step-by-step explanation:
all u gotta do is divide 6.4 by 4:)
hope that helps!<3
A rectangle has an area of 4x²-8x+3 square units. Which of the following could represent the perimeter of the rectangle in terms of x?
a. 2x-1
b. 2x-3
c. 4x-4
d. 8x-8
e. 10x-8
he local newspaper has letters to the editor from 30 people. If this number represents 2% of all of the newspaper's readers, how many readers does the newspaper have?
Doug started his math homework at 7:55 P.M. He finished all the problems at 8:15 P.M. How long did Doug spend doing his math homework?
Answer:
20 minutes
Step-by-step explanation:
If you add 20 minutes to 7:55 P.M., it becomes 8:15 P.M.
Answer:
20 minutos
Step-by-step explanation:
De 7:55 pm hasta las 8: pasaron 5 minutos, luego de 8:00 a 8:15 pm pasaron 15 minutos.
Así que sería 5 + 15 = 20 minutos
simpifly fully, does anyone know the answer.
Answer:
Step-by-step explanation:
Note : In multiplication if the bases are same u can add their exponent while in division if the bases are same u can subtract their exponent.
Hope this helps u !!
The picture is above I’ll mark as brainliest.
Answer:
?=5
Step-by-step explanation:
So let's do 16-6 (3*2)
10/2=5
Answer: ?=5
Step-by-step explanation:
In a rectangle the opposite sides are congruent (same length).
So we have ?+?+3+3=16
Let's use a variable for ?
x+x+3+3=16
Since there are 2 of the variable x we can write it as 2x since 2 of something means it's doubled. We can also combine 3 and 3.
2x+6=16
Let's subtract 6 from both sides.
[tex]2x+6-6=16-6\\2x=10[/tex]
Now let's divide both sides by 2 to find the value of x (which is ?)
[tex]\frac{2x}{2} =\frac{10}{2} \\x=5[/tex]
The value of x/? is 5.
Mrs. Law’s seventh grade class volunteers for two days at an animal shelter. Each day, 30% of students will be assigned to help groom animals, 50% will be assigned to walk animals, and 20% will be assigned to clean the kennels. Michaela designs a simulation to determine how likely it is that she will be assigned to walk animals both days. She assigns digits as follows:• 0, 1, 2 5 Grooming• 3, 4, 5, 6, 7 5 Walking• 8, 9 5 Cleaning Then she generates the following sets of random numbers for her simulation. 2, 9 5, 2 3, 9 0, 1 8, 3 0, 5 0, 5 8, 3 6, 8 4, 7 7, 4 1, 5 Based on the results of the simulation, what is the probability that Michaela will walk animals on: a. both days? b. one day only? c. at least one day?
Based on the results of the simulation, the probability that Michaela will walk animals on:
a. both days = 1/6
b. one day only = 2/3
c. at least one day = 5/6
What is probability?Probability is simply how likely something is to happen.
Grooming = 0, 1, 2
Walking = 3, 4, 5, 6, 7
Cleaning = 8, 9
Based on the data generated in simulation, categorizing it into "Michael will walk animals zero days/ one day only/ both days based on the digit categorization given above.
(2,9) - zero days
(5,2) - one day
(3,9) - one day
(0,1) - zero days
(8,3) -one day
(0,5) - one day
(8,3) - one day
(6,8) - one day
(4,7) - two days
(7,4) - two days
(1,5) - one day
Probability that Michaela will walk animals both days = [tex]\frac{2}{12} = \frac{1}{6}[/tex]
Probability that Michaela will walk animals one day only = [tex]\frac{8}{12} = \frac{2}{3}[/tex]
Probability that Michaela will walk animals at least one day = Probability that Michaela will walk animals one day only + Probability that Michaela will walk animals two days only = [tex]\frac{8}{12}+ \frac{2}{12} = \frac{10}{12} = \frac{5}{6}[/tex]
Learn more about probability here
https://brainly.com/question/11234923
#SPJ2
If f(x) = 5x² – 2x + 7 and g(x) = -2x2 +6x + 3
then f (x)-g(x) =
Answer:
7x² - 8x + 4
Step-by-step explanation:
f(x) - g(x)
= 5x² - 2x + 7 - (- 2x² + 6x + 3) ← distribute parenthesis by - 1
= 5x² - 2x + 7 + 2x² - 6x - 3 ← collect like terms
= 7x² - 8x + 4
help
dhgdfdfyfyfgfgfjfgfghfhgfdhgdfh
Answer:
5=26
14=17
n=1
31n=31*1=31
(PLEASE HELP 30 POINTS)
Select all the correct answers.
Liam owns some rectangular plots of land. All of the plots are the same length, x, and the width of each plot is 5 yards less than the length. The
total number of plots Liam owns is 20 more than the length of a plot. If the total area of all the plots Liam owns is 2,688 square yards, which
statements about the length of each plot are true?
The equation x3 - 15x2 - 100x - 2,688 0 can be used to find the length of each plot.
The equation x3 + 25x2 + 100% -2,688 = 0 can be used to find the length of each plot.
o o o o o
The equation x3 + 15x2 - 100x - 2,688 = 0 can be used to find the length of each plot.
The length of each plot is 12 yards.
The length of each plot is 8 yards.
Answer:
We have to:
"All of the plots are the same length, x"
L = x
"and the width of each plot is 5 yards less than the length"
W = x-5
"The total number of plots Liam owns is 20 more than the length of a plot"
20 + x
"the total area of all the plots Liam owns is 2,688 square yards"
A = (20 + x) * (x) * (x-5)
A = (20x - 100 + x ^ 2 -5x) * (x)
A = (x ^ 2 + 15x - 100) * (x)
2688 = (x ^ 3 + 15x ^ 2 - 100x)
x ^ 3 + 15x ^ 2 - 100x = 2688
x ^ 3 + 15x ^ 2 - 100x - 2688 = 0
Answer:
*** The equation x3 + 15x2 - 100x - 2.688 = 0 can be used to find the length of each plot.
Answer:x^3+15x^2-100x-2,688=0
Step-by-step explanation:
Solve for ABE
(It’s for geometry)
Answer:
<ABE = 109
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(sum of Intercepted Arcs)
< ABE = 1/2 ( 38+180)
< ABE = 1/2 (218)
<ABE = 109
Answer:
Formula: Half the sum of the two arcs. So, this would be the equation:
[tex]\frac{1}{2}[/tex][tex](38[/tex]+[tex]180[/tex])
Solve:
218 / 2 = 109
Answer: 109
The Titanus beetle can measure 16710 centimeters in length, and the Giant Weta beetle can measure 8510 centimeters in length. How much longer is the Titanus than the Giant Weta?
Answer:
The answer you're looking for is 8,200cm
Step-by-step explanation:
Is Your Eyes Good?
Can You Identify The Word
Answer:
No way its too blur XD
Step-by-step explanation:
sports
watching tv
reading books
surfing
and sleeping maybe
Answer:
Sports - 25%
Surfing - 25%
Reading Books - 20%
Watching TV - 25%
Malling - 5%
Step-by-step explanation:
There is a spinner with 12 equal areas, numbered 1 through 12. If the spinner is spun one time, what is the probability that the result is a multiple of 3 and a multiple of 4?
Answer:
1/12
Step-by-step explanation:
multiple of 3 and a multiple of 4 implies it can only be 12.
Since you only have the numbers from 1 to 12,
the prob(the 12) = 1/12
help ASAP ! it’s due soon
option
(c) is correct
Step-by-step explanation:
jsjsjd
pleaseeeee helppp meee!!!
Answer: 32x-48 should be your answer
Step-by-step explanation:
Answer:
32x - 48Step-by-step explanation:
-4(-8x + 12)
= -4 × (-8x) + (-4) × 12
= 32x + (-48)
= 32x - 48 (Ans)
