Use a table of values to find the solution to the equation f(x)=h(x) where
f (x) = 2/3-x and
h(x)= 3- 2x
Show your work
Answers
9514 1404 393
Answer:
x = 2 1/3
Step-by-step explanation:
We can examine the equations to see where the solution lies.
f(x) = (2/3) -x
This has an x-intercept where y=0, at x=2/3. It has a y-intercept where x=0, at y=2/3. Its slope is -1.
h(x) = 3 -2x
This has an x-intercept where y=0, at x=3/2. It has a y-intercept where x=0, at y=3. Its slope is -2.
__
In the first quadrant, the graph of h(x) is farther from the origin and steeper than the graph of f(x). The lines must cross in the 4th quadrant at some value of x that is greater than 3/2. The fraction in the definition of f(x) suggests that the solution will be a multiple of 1/3.
The attached table shows a couple of guesses at values of x that would make f(x) = h(x). We find that x = 7/3 is the solution we're looking for.
_____
Additional comment
Repetitive function evaluations are done conveniently and with fewer errors by a calculator or spreadsheet that can work with tables of values. Here, we have used a graphing calculator. These tools are readily available for free on almost any phone, tablet, or desktop computer platform.
Related Questions
2(3x – _) = 6x + 8 Using the distributive property, what would go in the blank in order for the given statement to be correct?
Answers
Answer:
2(3x - (-4)) = 6x + 8
Step-by-step explanation:
2(3x - A) = 6x + 8
6x - 2A = 6x + 8
Equating constant terms on both sides :
-2A = 8
A = -4
Therefore, 2(3x - (-4)) = 6x + 8
Answer:
Step-by-step explanation:
2(3x-(-4))=6x+8
2*3x=6x
2*-(-4)=8
Negative times negative makes positive 4
At the neighborhood block party, Hassan served 3 gallons of hot chocolate and 1/2 of a gallon of apple cider. How much more hot chocolate than apple cider did Hassan serve?
Write your answer as a fraction or as a whole or mixed number.
Answers
Answer:
2 gallons and 1/2
Step-by-step explanation:
You just have to subtract 1/2 from 3.
3 - 1/2 = 2 1/2
or
3 - .5 = 2.5
And 2 1/2 is how much more he served.
Answer: 5 times more hot chocolate
Step-by-step explanation:
X 4) Find the product of 4 x 2 3/4. 18 3/4 O 7 1/2 11 O 14
Answers
9514 1404 393
Answer:
11
Step-by-step explanation:
4 × (2 3/4) = 4×2 + 4×(3/4) = 8 + 3 = 11
or
4 × (2 3/4) = 4 × 11/4 = 11
Pls help 10 pts
X =
1
3
7
Answers
Answer:
3
Step-by-step explanation:
Answer:
x=3
Step-by-step explanation:
Secant-Secant Formula:(whole secant) x (external part) =
(whole secant) x (external part)
4 *(9) = x *(12)
36 =12x
Divide each side by 12
36/12 = 12x/12
3 =x
Which numbers are irrational? Select all that apply.
Answers
Answer:
I believe Option 1, 2 and 4 are all irrational numbers Hope this helps
Step-by-step explanation:
Help me PLEASEEEEEEEEEEEEE
Answers
Answer:
the first two are true and the last two are false
Corrie is 5 inches taller than Jason who is 4 ft. 9 in. Jennifer is
8 in, shorter than Corrie. How tall are Corrie and Jennifer?
(Express answers in simplest terms.)
Corrie___________.
Jennifer ___________.
Answers
Answer:
see below
Step-by-step explanation: 5 27 6 46
Corrie is 5 inches taller than Jason who is 4 ft. 9 in
Corrie must be 4 ft. 9 in + 5 in. = 5 ft. 2 in or convert ft to inches and add
[4(12) + 9] + 5 = 62 62/12 = 5 ft. 2 in.
Jennifer is 8 in, shorter than Corrie so Corrie is (5 - 8) inches (-3) inches taller than Jason or 3 in. shorter than Jason
Jennifer is 4 ft. 9 in - 3 in. = 4 ft. 6 in
Mrs. Smith decides to buy three sweaters and a pair of Jeans. She has $129 in her wallet.
If the price of the Jeans Is $40.05, what is the highest possible price of a sweater, each sweater is the
same price?
Variable:
Equation:
Solution:
Answers
Answer:
Step-by-step explanation:Herely/3fcEdSx's li[tex]^{}[/tex]nk to the answer:
bit.[tex]^{}[/tex]
I NEED HELP The measure of an angle is 74.6°. What is the measure of its supplementary angle?
Answers
Answer:
105.4º
Step-by-step explanation:
supplementary angles total 180º
180 - 74.6 = 105.4º
In a standard deck of cards, what is the probability of drawing a face card followed by drawing a non-face card
Answers
Answer:
0.1771
Step-by-step explanation:
total number of cards in a deck : 52
number of face card per suite : 3
total number of suites : 4 (hearts, clubs, diamonds, spades)
3 * 4 = total number of face cards
12/52 = 0.23 = probability of drawing a face card
remaining card are non face cards
52-12 = 40
40 non face cards
40/52 = 0.77 = probability of drawing a non face card
probability of drawing a face card followed by a non face card
multiply probabilities together to find combined probability
probability of drawing a face card * probability of drawing a non face card
= 0.23 * 0.77
= 0.1771
50 PTS AND BRAINLIEST FOR CORRECT ANSWER
Answers
Answer: I asked my teacher, she said it is c
Step-by-step explanation:
Answer:
yes it's c
have a great day
The zoo downtown has 9 times as many monkeys as elephants. They have 60 animals all together. How many elephants are there?
Answers
Answer:
6
Step-by-step explanation:
e = number of elephants
9 times as many monkeys as elephants
m = 9e
------------------------
60 animals all together
e + m = 60
e + 9e = 60
Combine like terms
10e = 60
Divide both sides by 10
e = 6
Answer: There’s technically no answer to this question, unless you specify that the zoo only has monkeys and elephants. If the zoo has more than two types of animal then the ratio doesn’t help because there are unknown variables.
However, if we knew that the zoo only has monkeys and elephants, then:
E = number of elephants
M = number of monkeys
M=9E
M + E = 60
9E+E= 60
10E = 60
E = 6
There are 6 elephants (and 54 monkeys).
8. True or False. The correlation coefficient is a measure of the strength of an
association between two variables.
Answers
Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is miles per hour, with a standard deviation of miles per hour. Estimate the percent of vehicles whose speeds are between miles per hour and miles per hour. (Assume the data set has a bell-shaped distribution.)
Approximately % of vehicles travel between 61 miles per hour and 71 miles per hour.
Answers
Answer:
68%
Step-by-step explanation:
We observe that the mean of the sample is (61+71)/2 = 66 mph which means the standard deviation of the sample is 5 because 66-5=61 and 66+5=71. The Empirical Rule states that for data observed in a normal distribution, 68% of data will fall within one standard deviation of the mean. Therefore, approximately 68% of vehicles travel between 61 miles per hour and 71 miles per hour.
Need help quick with full work
Answers
Answer:
(x + 5) and (x -1)
Step-by-step explanation:
Given
The attached graph
Required
The [tex]factors[/tex] of the graph
The x [tex]values[/tex] are where the [tex]curve[/tex] [tex]touches[/tex] the x-axis
The first is at:
[tex]x = -5[/tex]
Add 5 to both sides
[tex]x +5= -5+5[/tex]
[tex]x +5= 0[/tex]
This implies that the first factor is: (x + 5)
The second is at:
[tex]x =1[/tex]
Subtract 1 from both sides
[tex]x - 1 = 1 - 1[/tex]
[tex]x - 1 = 0[/tex]
This implies that the other factor is: (x - 1)
Given that sec0=-37/12 what is the value of cot0, for Pi/2<0
Answers
Answer:
Step-by-step explanation:
12/35
POSSIBLE POINTS 50
Mr Franklin needs to pay for his three kids to go to college. He figured out that college will cost an average of
$50,000 per year per child when they are ready to go to college. To pay for this, Mr. Franklin bought a cylindrical
gas truck, The truck is 40 feet long and the radius of the base is 60 inches, Gas has a density of five pounds per
cubic foot. Mr. Franklin makes $2.50 per pound of gas when he sends a delivery. How many trips of full tanks of
gas will Mr. Franklin have to send to pay for his three kids to go to four years of college each?
Be sure to label each step and show all work. Don't forget units.
a) Find the volume of the cylinder
b) Find the mass of the gas in one truckload by using the density formula
c) Find the amount of money one truckload will generate.
d) Find the amount of money four years of college will cost for Mr. Franklin's three children.
e) Find the amount of trips it will take Mr. Franklin to make enough money to pay for college,
5
x Clear
Und
Answers
Answer:
2500
Step-by-step explanation:
Question 3 of 25
If f(x) = 3x + 2, what is f(5)?
O A. 10
O B. 17
O c. 1
O D. 13
Answers
Answer:
I believe it's 17 :)
Step-by-step explanation:
5×3= 15 +2 = 17
I want to purchase a pair of sneakers for the summer. Champs and Footlocker
are selling the same pair of sneakers, but with different promotions. Champs
is offering a 25% off coupon and charging a tax of 8%. Footlocker is offering a
20% off coupon, but is not charging any tax.
If the sneakers have an original price of $80, where should I buy them
from if I want to spend the least amount of money?
Answers
Answer:
Champs is 64.8, Footlocker is 64. Footlocker is selling them for cheaper. You would go to Footlocker, as it's .8 off.
A radioactive substance decays to 30% of its original mass in 15 months. Determine the half-life of this radioactive substance to the nearest tenth. Show your work.
please help
Answers
Answer:
The half-life of this radioactive substance is of 8.6 months.
Step-by-step explanation:
Exponential decay of an amount:
The equation that models an amount after t units of time, subject to exponential decay, is given by:
[tex]A(t) = A(0)(1-r)^t[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
A radioactive substance decays to 30% of its original mass in 15 months.
This means that [tex]A(15) = 0.3A(0)[/tex]. We use this to find 1 - r.
[tex]A(t) = A(0)(1-r)^t[/tex]
[tex]0.3A(0) = A(0)(1-r)^{15}[/tex]
[tex](1-r)^{15} = 0.3[/tex]
[tex]\sqrt[15]{(1-r)^{15}} = \sqrt[15]{0.3}[/tex]
[tex]1 - r = (0.3)^{\frac{1}{15}}[/tex]
[tex]1 - r = 0.9229[/tex]
So
[tex]A(t) = A(0)(0.9229)^t[/tex]
Determine the half-life of this radioactive substance to the nearest tenth.
This is t for which A(t) = 0.5A(0). So
[tex]A(t) = A(0)(0.9229)^t[/tex]
[tex]0.5A(0) = A(0)(0.9229)^t[/tex]
[tex](0.9229)^t = 0.5[/tex]
[tex]\log{(0.9229)^t} = \log{0.5}[/tex]
[tex]t\log{0.9229} = \log{0.5}[/tex]
[tex]t = \frac{\log{0.5}}{\log{0.9229}}[/tex]
[tex]t = 8.6[/tex]
The half-life of this radioactive substance is of 8.6 months.
PLEASE ANSWER THIS
PLEASE URGENT WORK
I M CRYING
Answers
Answer:
b=69(alternate angle)
b=37(alternate angle)
Plz help me well mark brainliest if correct
Answers
Answer:
I think it is b) 70
Step-by-step explanation:
Arrange the numbers in ascending order then find the middle number.
Answer:
70
Step-by-step explanation:
Write down all the data points: 20, 40, 50, 70, 80, 90, 110 and identify which is in the very middle.
Only please help #2,3,5, and 6
Answers
3)5.30/6= 0.88
5)3:4
6)a) 15:20 and to simply divide by 5 to get 3:4
b)the amount saved is 5 (20-15) so the first ratio is 5:20 and to simplify divide 5 to get 1:4
Answer:
3.$0.9
5.9:3 =3:1
Step-by-step explanation:
3.$5.40÷6=$0.9
Someone please help me
Answers
Answer:
48
Step-by-step explanation: 1 foot is 12 inches. Since the feet are going up by ones, you can say 1=12, 2=24 (+12), 3=36(+12), 4=48(+12)
Hope this helps
Answer and Step-by-step explanation:
The answer is 48.
Each value of y is a multiple of 12, so for when there is 4 feet, you multiply 12 by 4 to get 48.
For when it is 1 foot, you multiply 12 by 1 to get 12.
For when it is 2 feet, you multiply 12 by 2 to get 24.
For when it is 3 feet, you multiply 12 by 3 to get 36
For when it is 5 feet, you multiply 12 by 5 to get 60.
If you were to continue, the y-values (aka the inches) will always be a multiple of 12.
#teamtrees #PAW (Plant And Water)
A snail can travel 390 inches in 5 hours.
How far does it travel in 1 hour?
Answers
Answer:
78 inches
Step-by-step explanation:
5 hours = 390 inches
1 hour = 390 / 5
1 hour = 78 inches
Therefore the snail travels 78 inches in 1 hour.
Hope this helps!
You answered 85% of the questions on the quiz correctly. What fraction of
the questions did you answer correctly?
Answers
Answer:
A percentage is out of 100.
85/100
in lowest terms this is
17/20
Hope this helps :)
Step-by-step explanation:
Given the point (18, -10), apply the rule and tell the image after the translation as an ordered pair with no spaces.
(x,y) --> (x - 11, y - 9)
Answers
Answer:
The answer is (7,-19)
Step-by-step explanation:
Remember, 18 is x, and -10 is y. The rule says to subtract 11 from 18, which would be 7. For y, you add -9 to -10, which would be -19.
Therefore, your answer should be (7,-19)
Hope this helps!
By applying the rule and image after the translation as an ordered pair with no spaces is the point (7, -19).
What is translation?Translation is a term used in geometry to describe a function that moves an object a certain distance. The object is not altered in any other way.
Given point = (18, -10)
(x, y) --> (x - 11, y - 9)
(18, -10) = (18 - 11, -10 - 9)
New point = (7, -19)
Hence, by applying the rule and image after the translation as an ordered pair with no spaces is the point (7, -19).
Learn more about translation here
https://brainly.com/question/20426179
#SPJ2
GUYS PLEASE HELP ALMOST DUE
Answers
Answer:
1/5
Step-by-step explanation:
y = 12
12 = 1/5 x 60
12= 12
y = 9
9 = 1/5 x 45
9 = 9
and so on and it always results to one fifth
Suppose you are investigating the relationship between two variables, traffic flow and expected lead content, where traffic flow is a predictor of lead content. You find the 95% CI for expected lead content when traffic flow is 15, based on a sample of n= 10 observations, is (461.7, 598.1).
Required:
What parameter is this interval estimating?
Answers
Answer:
The answers is " Option B".
Step-by-step explanation:
[tex]CI=\hat{Y}\pm t_{Critical}\times S_{e}[/tex]
Where,
[tex]\hat{Y}=[/tex] predicted value of lead content when traffic flow is 15.
[tex]\to df=n-1=8-1=7[/tex]
[tex]95\% \ CI\ is\ (463.5, 596.3) \\\\\hat{Y}=\frac{(463.5+596.3)}{2}\\\\[/tex]
[tex]=\frac{1059.8}{2}\\\\=529.9[/tex]
Calculating thet-critical value[tex]t_{ \{\frac{\alpha}{2},\ df \}}=-2.365[/tex]
The lower predicted value [tex]=529.9-2.365(Se)[/tex]
[tex]463.5=529.9-2.365(Se)\\\\529.9-463.5=2.365(Se)\\\\66.4=2.365(Se)\\\\Se=\frac{66.4}{2.365} \\\\Se=28.076[/tex]
When [tex]99\%[/tex] of CI use as the expected lead content: [tex]\to 529.9\pm t_{0.005,7}\times 28.076 \\\\=(529.9 \pm 3.499 \times 28.076)\\\\=(529.9 \pm 98.238)\\\\=(529.9-98.238, 529.9+98.238)\\\\=(431.662, 628.138)\\\\=(431.6, 628.1)[/tex]
Drag the tiles to the boxes to form correct pairs.
Match the values associated with this data set to their correct descriptions.
{6, 47, 49, 15, 43, 41, 7, 36}
First quartile, 11
Median, 45
Third quartile, 38.5
Difference of largest value and median, 10.5
Answers
Answer:
Step-by-step explanation: