Answers
looking at the picture, the region AB is where the inequality of f(x) overlaps the inequality g(x), so if we pick any point on that blue region AB, then f(x) will be TRUE and g(x) will also be TRUE, lemme narrow it down some, let's pick the point on AB of say (0,0), namely x = 0 and y = 0
let's try the 1st set
0 ⩽ - 2(0) + 3
0 ⩽ 3 <--- is that true? well yes, zero is less or equals, actually less than 3
0 ⩽ 0 + 3
0 ⩽ 3 <--- is that true? yes it's
let's try the 2nd inequalities set with the same values for "x" and "y"
0 ⩾ -2(0) + 3
0 ⩾ 3 <--- is that true? nope, no dice
let's not bother checking the other, since it already gave FALSE
let's try the 3rd inequalities set, same values
0 ⩽ -3(0) + 2
0 ⩽ 2 <--- is that true? yeap
0 ⩽ -(0) + 2
0 ⩽ 2 <---- is that true? yeap
not to bother you with the 4th set one, the 4th one fails and gives FALSE
so we know the 1st and 3rd one give TRUE on for f(x) and g(x), so which one is it?
take a peek at the picture below, notice the rise and run and therefore the slopes for each, g(x) has a slope of 2/2 = 1, and f(x) has a slope of 3/1 = 3, both going downwards, so both are negative, namely -1 and -3.
that means that g(x) will look like -1x + something, or -x + something.
and means that f(x) will look like -3x + something.
so that means the only set with those slopes will be [tex]\begin{cases} y\leqslant -3x + 2\\ y \leqslant -x + 2 \end{cases}[/tex]
Related Questions
Find the measure of the incanted angle to the nearest degree
Answers
Answer:
15.4 degrees
Step-by-step explanation:
b= 53
h = 55
cos -¹( 53/53)= 15.4
Your true height is 70.2 inches. A laser device at a health clinic that gives measurements to thenearest hundredth reads your height as 71.05 inches. A tape measure gives reading to the nearest haftinches gives your height as 69.5 inches. State which measurement is more precise and which measurementis more accurate and explain why.
Answers
Answer:
Accuracy = Tape measurement.
Precision = Laser measurement
Step-by-step explanation:
Given that :
True height, = 70.2 inches
Laser measured height = 71.05 (nearest hundredth)
Tape measured height = 69.5 - nearest half inch.
Accuracy simply means how close a measured value is to the true value of the measurement. ;
True height - tape measurement
70.2 - 69.5 = 0.7
True measurement - laser measurement :
|70.2 - 71.05| = 0.85
Fron the difference in the values, the measurement which is closer to the true height is the tape measurement.
However, in terms of detail in the measured value, the laser measure value is expressed to the nearest hundredth, hence giving it more precision over the tape measured value.
The product of 10 and the difference between 8 and -9?
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
170
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\text{The phrase can be rewritten as:}\\\\10 * (8-(-9))\\---------------\\\rightarrow 8-(-9) = 8 + 9 = 17\\\\\rightarrow 10 * 17\\\\\rightarrow \boxed{170}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Angelica’s bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink what fraction of the bouquet is pink? There are 12 roses in a dozen.
A. 5/12
B. 7/12
C. 5/7
D. 7/5
Answers
Answer:
7/12
Step-by-step explanation:
There are 12 roses - 5 white = 7 pink
7 pink / 12 total
The length of a rectangle is 10 yd less than three times the width, and the area of the rectangle is 77 yd^2. Find the dimensions of the rectangle.
Answers
Answer:
width = 7, length = 11
Step-by-step explanation:
area = 77
length = 3w - 10
width = w
w(3w - 10) = 77
3w^2 - 10w - 77 = 0
(3w + 11)(w - 7) = 0
we rule out 3w + 11 = 0 because w would be negative
so we use w - 7 = 0
so the width = 7
length = 3w - 10
length = 21 - 10
length = 11
13. 30 of the 100 iPads in an inventory are known to be cracked. What
is the probability you randomly select one that is not cracked?
Answers
Answer:
7/10 or 0.7
Step-by-step explanation:
a probability is always the ratio of possible cases over all cases.
"all cases" here is 100.
possible cases are all iPads not cracked in the inventory = 70 (because 30 are cracked, that leaves 100-30=70 not cracked).
so, the probability to select a non-cracked unit is
70/100 or simplified 7/10 (or 0.7)
what is 6 3/5 - 4 3/10
Answers
Answer:
2 3/10
Step-by-step explanation:
3/5x2=6/10
6/10-3/10=3/10
Please help!
Answers
A,B,C and D
The information is already in the chart
( ignore the charts below question 2.)
Answers
I believe the answer is B!
Hope this helped you! Please follow my account, thanks!
A ball is thrown from an initial height of 4 feet with an initial upward velocity of 40 feet per second. The ball's height h (in feet) after t seconds is given by the following. h=4+40t-16t2 Find all values of for which the ball's height is 26 feet.
Answers
Answer:
Step-by-step explanation:
To find the times that the height is 26 feet, we set the position equation equal to 26 and solve for t:
[tex]26=-16t^2+40t+4[/tex] and
[tex]0=-16t^2+40t-22[/tex] and factor that however you are factoring in class to solve a problem like this. When you do that you get
t = .86 seconds and t = 1.68 seconds. That means that .86 seconds after the ball is thrown into the air, it reaches a height of 26 feet; it goes up to its max height and then gravity takes over and pulls it back down. When this happens, it will pass 26 feet again on its way back down. This second time is after 1.68 seconds.
Use the ratio of a 45-45-90triangle to solve for the variables. Make sure to simplify radicals. Leave your answers as radicals in simplest form.
Answers
9514 1404 393
Answer:
m = n = 5
Step-by-step explanation:
The side ratios in a 45°-45°-90° triangle are 1 : 1 : √2. That is, the hypotenuse is √2 times the side length. Here, the hypotenuse is 5√2, so the side length must be 5.
m = n = 5
6 less than six times a number is 42 what is the number
Answers
Answer:
x = 8
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
6x - 6 = 42
Step 2: Solve for x
[Addition Property of Equality] Add 6 on both sides: 6x = 48[Division Property of Equality] Divide 6 on both sides: x = 8Answer: -6
Step-by-step explanation:
We can create an equation based on the info given.
6-6x=42 Now you solve for x, the unknown number.
-6 -6 Subtract 6 on both sides
-6x=36
/-6 /-6 Divide by -6 on both sides
x=-6
The number is -6.
Put the following equation of a line into slope-intercept form, simplifying all fractions 2x-2y=14
Answers
y = x - 7
Step-by-step explanation:
Answer: y = x - 7
Slope intercept form: y = mx + b
[tex]2x-2y=14\\\\-2y=-2x+14\\\\y=\frac{-2x+14}{-2} =\frac{-2(x-7)}{-2} =x-7[/tex]
Determine what type of transformation is represented.
A. none of these
B. reflection
C. dilation
D. rotation
Answers
Answer:
The answer is "Option D"
Step-by-step explanation:
In a rotation, an item is rotated around with a known location. Clockwise or anticlockwise spinning is possible. Rotation centers are spherical geometry in space where rotation occurs. The direction of inclination is the indicator of the total rotation made. Rotary point refers to that part point of a figure around which it is revolved.
5+(-7)=
A-12
B
-2
с
2
D
12
E
none of these
Answers
Answer:
-2
Step-by-step explanation:
5 + (-7)
Since the 7 is larger than 5, the 7 will overpower the 5 in a way. So, all you do is subtract 7 and 5.
7 - 5 = 2
But the 7 has a negative with it (since it's larger), so you add the negative to the 2.
7 - 5 = -2
The answer will be -2.
Given parallelogram RUST and m< RUT=43, what other angle has the same measurement
Answers
9514 1404 393
Answer:
(b) ∠STU
Step-by-step explanation:
Transversal UT between parallel sides RU and ST creates alternate interior angles RUT and STU. These are congruent.
∠STU has the same measure as ∠RUT
_____
The figure shown is a trapezoid, not a parallelogram.
The maximum and minimum values of a quadratic function are called as________of the function.
Answers
Vertex is the point where the function is at its maximum/ minimum.
A tank contains 9,000 L of brine with 18 kg of dissolved salt. Pure water enters the tank at a rate of 90 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate.
(a) How much salt is in the tank after t minutes?
(b) How much salt is in the tank after 20 minutes?
Answers
Let x(t) denote the amount of salt (in kg) in the tank at time t. The tank starts with 18 kg of salt, so x (0) = 18.
The solution is drained from the tank at a rate of 90 L/min, so that the amount of salt in the tank changes according to the differential equation
dx(t)/dt = - (x(t) kg)/(9000 L) × (90 L/min) = -1/100 x(t) kg/min
or, more succintly,
x' = -1/100 x
This equation is separable as
dx/x = -1/100 dt
Integrating both sides gives
∫ dx/x = -1/100 ∫ dt
ln|x| = -1/100 t + C
x = exp(-1/100 t + C )
x = C exp(-t/100)
(a) Using the initial condition x (0) = 18, we find
18 = C exp(0) ==> C = 18
so that
x(t) = 18 exp(-t/100)
(b) After 20 minutes, we have
x (20) = 18 exp(-20/100) = 18 exp(-1/5) ≈ 14.74
so the tank contains approximately 14.74 kg of salt after this time.
Solve |6k + 12| + 9 = 9 for k.
Answers
Step-by-step explanation:
6k + 12 + 9=9
6k + 12 = 9 - 9
6k + 12 = 0
12 = -6k
12/-6 = -6k/-6
2/-1 = k
k = -2
Answer:
k=-2
Step-by-step explanation:
6k+12+9=9
subtract 9 from both sides
6k+12=0
subtract 12 from not sides
6k= -12
divide both sides by 6 (isolating the variable)
k= -12/6
simplify
k= -2
For the same random sample of adult women, with a sample mean height of x¯=64.3 inches and sample standard deviation of s=2.4 inches, use the Empirical Rule to determine the approximate percent of heights that lie between 59.5 inches and 69.1 inches.
Round your answer to the nearest whole number (percent).
Answers
Answer:
95%
Step-by-step explanation:
Mean , xbar = 64.3; standard deviation, s= 2.4
Using the empirical formula where ;
68% of the distribution is within 1 standard deviation from the mean ;
95% of the distribution is within 2 standard deviation from the mean
percent of heights that lie between 59.5 inches and 69.1 inches.
Number of standard deviations from the mean /
Z = (x - μ) / σ
(x - μ) / σ < Z < (x - μ) / σ
(59.5 - 64.3) / 2.4 < Z < (69.1 - 64.3) / 2.4
-2 < Z < 2
Thia is within 2 standard deviations of the means :
2 standard deviation form the mean = 95% according to the empirical rule.
Which one is it------------------
Answers
Answer:
you're right
Step-by-step explanation:
As the number of copies increases, the dimensions of the images continue to decrease but never reach 0. Option A is correct.
As of the given statement,
Both copy machines reduce the dimensions of images that run through the machines. which statment is true is to be justified.
In mathematics, dimensions are the measurements of the size or distance of an item, region, or space in one direction. In layman's words, it is the measurement of something's length, width, and height. Length is the most commonly used dimension.
here,
Both copy machines diminish the size of images that pass through them. Which statement is correct must be justified. So, As the number of copies increases, the image dimensions drop but never reach zero.
Thus, the image dimensions decrease as the number of copies grows, but never reaches zero.
Learn more about dimensions here:
https://brainly.com/question/28688567
#SPJ2
poonam wants to invest in an account today
to have $4000 at the end of 8 years.
If she can invest at 4.25% Compounded
Semi-annually, how much does she need
to invest?
Answers
Answer:
2055.15
Step-by-step explanation:
A(1+r)^n=4000
A is the money that she need to invest
r is rate
n is the time( depend on monthly or yearly rate)
A(1+4.25%)^16=4000
A=2055.15
The circle graph above shows the distribution of utility expenses for the Hierra family last year. If the family’s total utility expenses last year were $3,600, what were their expensive go water and sewer.
Water and sewer=X%
Electric=30%
Heating and gas=50%
Answers
Answer:
The correct answer is - $720 or 20%.
Step-by-step explanation:
Given:
Total expense = 3600
Electric=30%
Heating and gas=50%
Water and sewer=X%
Solution:
For electric: 3600*30/100 = 1080
for heating and gas: 3600*50/100 = 1800
Left money for expense of water and shower = total - (electric and heating)
= 3600-1880
= 720
Percentage of water and shower = 720*100/3600
= 20%
Answer:
Correct!
Step-by-step explanation:
Thank you this is correct :) I took the test
A certain university has 25,000 registered students. To estimate the percentage who are living at home, a simple random sample of 400 students is drawn. It turns out that 317 of them are living at home. Now, 317 out of 400 is (about) 79%. Indicate whether each quantity is actual or estimated from the data. You'll get partial credit for
Answers
Answer:
Indication of Actual Quantity and Estimated Quantity
Actual Quantity:
Registered students in the university = 25,000
Sample of students = 400
Students living at home = 317
Estimated Quantity:
317 out of 400 students
79%
Step-by-step explanation:
An actual quantity does not require to be estimated. It is usually given in the question or scenario. For example, the number of registered students in the university is an actual quantity. The percentage of students who live at home from the simple random sample of 400 is an estimated quantity.
Silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. The success of the procedure depends on various biomechanical properties of the human nasal periosteum and fascia. An article reported that for a sample of 10 (newly deceased) adults, the mean failure strain (%) was 24.0, and the standard deviation was 3.2.
Required:
a. Assuming a normal distribution for failure strain, estimate true average strain in a way that converys information about precision and reliability.
b. Predict the strain for a single adult in a way that conveys information about precision and reliability. How does the prediction compare to the estimate calculated in part (a)?
Answers
Solution :
Given information :
A sample of n = 10 adults
The mean failure was 24 and the standard deviation was 3.2
a). The formula to calculate the 95% confidence interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times \frac{s}{\sqrt n}$[/tex]
Here, [tex]$t_{\alpha/2,n-1} = t_{0.05/2,10-1}$[/tex]
= 2.145
Substitute the values
[tex]$24 \pm 2.145 \times \frac{3.2}{\sqrt {10}}$[/tex]
(26.17, 21.83)
When the [tex]\text{sampling of the same size}[/tex] is repeated from the [tex]\text{population}[/tex] [tex]n[/tex] infinite number of [tex]\text{times}[/tex], and the [tex]\text{confidence intervals}[/tex] are constructed, then [tex]95\%[/tex] of them contains the [tex]\text{true value of the population mean}[/tex], μ in between [tex](26.17, 21.83)[/tex]
b). The formula to calculate 95% prediction interval is given by :
[tex]$\overline x \pm t_{\alpha/2,-1} \times s \sqrt{1+\frac{1}{n}}$[/tex]
[tex]$24 \pm 2.145 \times 3.2 \sqrt{1+\frac{1}{10}}$[/tex]
(31.13, 16.87)
Anyone knows the answer?
Please!
Answers
Answer:
C
Step-by-step explanation:
sin(theta)=7/8, theta=arcsin(7/8)=61
Decompose -6x/(x+2)(x+8) into partial fractions.
Answers
The partial fraction expansion takes the form
-6x/((x + 2) (x + 8)) = a/(x + 2) + b/(x + 8)
Both factors in the denominator are linear, so the numerators in the corresponding partial fractions have degree 1 - 1 = 0 and are thus constants.
Combine the fractions on the right side into one with a common denominator, then set the numerators on both sides of the equation equal to each other:
-6x = a (x + 8) + b (x + 2)
Expand the right side and collect terms by powers of x :
-6x = (a + b) x + (8a + 2b)
It follows that
a + b = -6 and 8a + 2b = 0
==> a = -2 and b = 8
So we end up with
-6x/((x + 2) (x + 8)) = -2/(x + 2) + 8/(x + 8)
What is the value of -
-X2 - 4x – 11 if x = -3?
Answers
An expression is shown below:
10n3 − 15n2 + 20xn2 − 30xn
Part A: Rewrite the expression so the GCF is factored completely. (4 points)
Part B: Rewrite the expression completely factored. Show the steps of your work.
Answers
Answer:
An expression is shown below:
10n³− 15n² + 20xn² − 30xn
Part A: Rewrite the expression so the GCF is factored completely. (4 points)
10n³− 15n² + 20xn² − 30xn
2*5*n*n*n-5*3*n*n+2*5*2*x*n*n-2*5*3*x*n
Greatest common factor=5*n=5n
Part B: Rewrite the expression completely factored. Show the steps of your work.
Solution given;
10n³− 15n² + 20xn² − 30xn
5n(2n²-3n+4xn-6x)
5n(2n²+4xn-3n-6x)
5n(2n(n+2x)-3(n+2x))
5n(n+2x)(2n-3)
Answer:
[tex]5n(2n-3)(n+2x)[/tex]
Step-by-step explanation:
Step 1: Rewrite the expression so the GCF is factored completely
[tex]10n^{3} - 15n^{2} + 20xn^{2} - 30xn[/tex]
The GCF is 5n so factor it out
[tex]5n(2n^{2} - 3n + 4xn - 6x)[/tex]
Step 2: Rewrite the expression completely factored
[tex]5n(2n^{2} - 3n + 4xn - 6x)[/tex]
[tex]5n(2n(n+2x)-3(n+2x))[/tex]
[tex]5n(2n-3)(n+2x)[/tex]
Answer: [tex]5n(2n-3)(n+2x)[/tex]
Julie is tracking the growth of a plant for a science project. The height of the plant on the 2nd day she measured was 8 inches and on the 7th day it was 20.5 inches. Assume the relationship is linear
Answers
Answer:
Step-by-step explanation:
The relationship is linear, so the plant grows the same amount each day.
The height on the 2nd day was 8 inches:
h₂ = 8
The height on the 7th day was 20.5 inches:
h₇ = h₂ + (7-2)d = 8 + 5d = 20.5
d = 2.5
The plant grows 2.5 inches each day.
PLEASE HELP
Write the equation of the line that is perpendicular to the given segment and that passes through the point (-6, -3). A. 1 V=--x-3 2 B. 1 V=--X-6 2 C. y = 2x + 9 D. = 2x-6.
Answers
Answer:
C
Step-by-step explanation:
The slope of the line will be (2) and the equation will be C
