Which ordered pairs are in the solution set of the system of linear inequalities?
y > Negative one-thirdx + 2
y < 2x + 3
On a coordinate plane, 2 straight lines are shown. The first solid line has a negative slope and goes through (0, 2) and (6, 0. Everything to the right of the line is shaded. The second dashed line has a positive slope and goes through (negative 3, negative 3) and (0, 3). Everything above the line is shaded.
Answers
Options:
(2, 2), (3, 1), (4, 2)
(2, 2), (3, –1), (4, 1)
(2, 2), (1, –2), (0, 2)
(2, 2), (1, 2), (2, 0)
Answer:
A. (2, 2), (3, 1), (4, 2)
Step-by-step explanation:
Given
[tex]y > -\frac{1}{3}x + 2[/tex]
[tex]y < 2x + 3[/tex]
Required
Solve for x and y
To solve this, we make use of graphical method (see attachment for graph)
All points that lie on the shaded region are true for the inequality
Next, we plot each of the given options on the graph
A. (2, 2), (3, 1), (4, 2)
All 3 points lie on the shaded region.
Hence, (a) is true
Answer:
A. (2, 2), (3, 1), (4, 2)
Step-by-step explanation:
Related Questions
SCALCET8 3.9.017.MI. Two cars start moving from the same point. One travels south at 48 mi/h and the other travels west at 20 mi/h. At what rate is the distance between the cars increasing two hours later
Answers
Answer:
The rate at which the distance between the cars increasing two hours later=52mi/h
Step-by-step explanation:
Let
Speed of one car, x'=48 mi/h
Speed of other car, y'=20 mi/h
We have to find the rate at which the distance between the cars increasing two hours later.
After 2 hours,
Distance traveled by one car
[tex]x=48\times 2=96 mi[/tex]
Using the formula
[tex]Distance=Time\times speed[/tex]
Distance traveled by other car
[tex]y=20\times 2=40 mi[/tex]
Let z be the distance between two cars after 2 hours later
[tex]z=\sqrt{x^2+y^2}[/tex]
Substitute the values
[tex]z=\sqrt{(96)^2+(40)^2}[/tex]
z=104 mi
Now,
[tex]z^2=x^2+y^2[/tex]
Differentiate w.r.t t
[tex]2z\frac{dz}{dt}=2x\frac{dx}{dt}+2y\frac{dy}{dt}[/tex]
[tex]z\frac{dz}{dt}=x\frac{dx}{dt}+y\frac{dy}{dt}[/tex]
Substitute the values
[tex]104\frac{dz}{dt}=96\times 48+40\times 20[/tex]
[tex]\frac{dz}{dt}=\frac{96\times 48+40\times 20}{104}[/tex]
[tex]\frac{dz}{dt}=52mi/h[/tex]
Hence, the rate at which the distance between the cars increasing two hours later=52mi/h
Pls help quick:
The following figures are not drawn to scale but
AB and CD (if present in the picture) are straight lines. Find x:
Answers
Step-by-step explanation:
2x+60°= 110°
2x= 110-60
2x= 50
x= 25°
please help me now I need it please this is calculuse
Answers
Answer:
none of these
Step-by-step explanation:
If you have 3/8 of one pie, what does the denominator tells you ?
Answers
Step-by-step explanation:
There was originally 8 pieces of pie.
Answer:
if you have 3/8 of one pie, the denominator tells you that the pie was divided into 8 piece.
In the diagram, point D is the center of the medium-sized circle that passes through C and E, and it is also the center of the largest circle that passes through A and G. Each of the diameters of the small circles with centers B and F equals the radius of the medium-sized circle with center D. The shaded area is what fraction of the largest circle?Single choice.
Answers
9514 1404 393
Answer:
5/8
Step-by-step explanation:
The area of the smaller circles is proportional to the square of the ratio of their diameters. The two smallest circles have diameters equal to 1/4 the diameter of the largest circle. Hence their areas are (1/4)^2 = 1/16 of that of the largest circle.
Similarly, the medium circle has a diameter half that of the largest circle, so its area is (1/2)^2 = 1/4 of the are of the largest circle.
The smaller circles subtract 2×1/16 +1/4 = 3/8 of the area of the largest circle. Then the shading is 1-3/8 = 5/8 of the area of the largest circle.
Estimate 19.625-6.77 by first rounding each number to the nearest tenth.
Answers
Answer:
13
Step-by-step explanation:
1. Round 19.625 up to 20.
2. Round 6.77 up to 7.
3. Calculate the equation. Ans is 13.
How can you use transformations to graph this function?
Answers
Answer:
What function?
Step-by-step explanation:
5. In 2015, Texas led the nation in the percentage of people who lacked health insurance (21.6% of the population). It is known that, nationally, 5% of patients account for 50% of the costs of healthcare. These are the “high cost” patients Assume* that: Being a high cost patient and being uninsured are independent characteristics Insured and uninsured people become “patients” at the same rate The uninsured and high cost patients in Texas are evenly distributed across the state, and that high cost patients are evenly distributed across insured and uninsured patient populations a. What is the probability that a patient in a Texas healthcare facility will be a high cost patient who is uninsured?
Answers
Answer: 0.108
Step-by-step explanation:
Since the probability of the uninsured is 21.6% of the population, then the probability of insured will be:
= 1 - 21.6%
= 78.4%
The probability of high cost patients is 5%. Therefore, the probability that a patient in a Texas healthcare facility will be a high cost patient who is uninsured will be:
= 5% × 21.6%
= 0.05 × 0.216
= 0.108
Because of high tuition costs at state and private universities, enrollments at community colleges have increased dramatically in recent years. The following data show the enrollment (in thousands) for Jefferson Community College for the nine most recent years.
Year Period (t) Enrollment (1,000s)
2001 1 6.5
2002 2 8.1
2003 3 8.4
2004 4 10.2
2005 5 12.5
2006 6 13.3
2007 7 13.7
2008 8 17.2
2009 9 18.1
Required:
a. What type of pattern exists in the data?
b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
c. What is the forecast for year 10?
Answers
Answer:
a. A linear pattern exists in the data.
b. The parameters for the line that minimizes MSE for this time series are as folows:
ß1 = Estimated slope = 1.4567
ß0 = Estimated intercept = 4.7165
Also, we have:
MSE = Mean squared error = 0.4896
c. Forecast for year 10 is 19,280.
Step-by-step explanation:
a. What type of pattern exists in the data?
Note: See Sheet1 of the attached excel file for the line graph.
From the line graph, it can be observed that a linear pattern exists in the data.
b. Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series.
Note: See Sheet2 of the attached excel file for all the calculations to obtain the following:
Sample size = 9
Total of X = 45
Total of Y = 108
Mean of X = Total of X / Sample size = 45 / 9 = 5
Mean of Y = Total of X / Sample size = 108 / 9 = 12
SSxx = Total of (X - Mean of X)^2 = 60
SSyy = Total of (Y - Mean of Y)^2 = 130.74
SSxy = Total of (X - Mean of X) * (Y - Mean of Y) = 87.40
Therefore, we have:
ß1 = Estimated slope = SSxy/SSxx = 87.4 / 60 = 1.4567
ß0 = Estimated intercept = Mean of Y – (ß1 * Mean of X) = 12 - (5 * 1.4567) = 4.7165
Therefore, the parameters for the line that minimizes MSE for this time series are as folows:
ß1 = Estimated slope = 1.4567
ß0 = Estimated intercept = 4.7165
Regression equation which also used in the attached excel is as follows:
Y = ß0 + ß1X =
Y = 4.7165 + 1.4567X …………………. (1)
SSE = Sum of squared error = Total of (Y - Y*)^2 = 3.4273
Therefore, we have:
MSE = Mean squared error = (SSE/(n-2)) = (3.4273 / (9 - 2)) = 0.4896
c. What is the forecast for year 10?
This implies that X = 10
Substitute X = 10 into equation (1), we have:
Y = 4.7165 + (1.4567 * 10) = 19.28
Since it is 1,000s, we have:
Y = 19.28 * 1,000 = 19,280
Therefore, forecast for year 10 is 19,280.
GM projected that 3% of their cars produced this year will be defective. If GM produced 1,698 cars that were defective, how many cars did GM produce this year
Answers
Answer:
56600 cars
Step-by-step explanation:
Below is the calculation of number of cars produced.
The percentage of cars that is defected = 3%
Number of cars that are defective = 1698 cars
The number of cars produced in a year = 1698 / 3%
The number of cars produced in a year = 56600 cars
You need
1
1
4
feet of string to make 20 holiday ornaments.
To make 14 holiday ornaments, you will need
feet of string.
Answers
Answer:
79.8
Step-by-step explanation:
math
Greatest to least 2,250 2,700 2,450 2,500
Answers
Answer:
sorting;
2,7002,5002,450 2,250greatest = 2,700
least = 2,250
HAVE A NİCE DAY
Step-by-step explanation:
GREETINGS FROM TURKEY ツ
2,500
2,450
least: 2,250
NO LINKS OR ANSWERING WHAT YOU DON'T KNOW?
4. Suppose y varies inversely with the x, and y = -1 when = 3. What inverse variation equation relates x and y?
a. y = 3/x
b. b. y = -3x
c. y = 3x
d. y = -3/x
5. Suppose y varies inversely with x and y = 68 when x = 1/17. What is the value of x when y = 16?
a. 64
b. 32
c. 1/4
d. 1/16
6. Suppose y varies inversely with x, and y = 5 when x = 15. What is the value of y when x = 25
a. 3
b. 5
c. 25
d. 15
Answers
Answer:
4,a
5.d
6.c
plz mark me as brainliest
Step-by-step explanation:
Answer:
1. A
2. C
3. A
Step-by-step explanation:
all the explanations are In the image above
From the table below, determine whether the data shows an exponential function. Explain why or why not.
x
3
2
1
–1
y
8
2
0.5
0.125
a. No; the domain values are at regular intervals and the range values have a common factor 0.25. b. No; the domain values are not at regular intervals although the range values have a common factor. c. Yes; the domain values are at regular intervals and the range values have a common factor 4. d. Yes; the domain values are at regular intervals and the range values have a common factor 0.25.
Answers
9514 1404 393
Answer:
b. No; the domain values are not at regular intervals although the range values have a common factor.
Step-by-step explanation:
The differences between x-values are ...
-1, -1, -1, -2 . . . . not a constant difference
The ratios of y-values are ...
2/8 = 0.5/2 = 0.125/0.5 = 0.25 . . . . a constant difference
The fact that the domain values do not have a common difference renders the common factor of the range values irrelevant. The relation is not exponential.
The point-slope form of a line that has a slope of -2 and passes through point (5,-2) is shown below.
y+2=-2(x-5)
What is the equation in slope-intercept form?
O y=-2x+12
O y=-2x+8
O y=-22-7
O y=-2x-3
Savait
Answers
Answer:
y = -2x + 8Step-by-step explanation:
The equation in slope-intercept form: y = mx + b
y + 2 = -2(x - 5)
y + 2 = -2x + 10 {subtract 2 from both sides
y = -2x + 8
The mean of 19 numbers is 1600. If 2000 is added in the number. Find the new mean
Answers
Answer:
Here's your answer .
hope it helps you
Given right angle ABC, what the value of tan(A)?
5/13
12/13
12/5
13/12
need answer asap
Answers
Hi there!
[tex]\large\boxed{12/5}}[/tex]
tan (angle) = Opposite side / Adjacent side, so:
Tan (A) = opposite side / adjacent side
= 24 / 10
Simplify:
= 12 / 5
Can someone help asap?
Answers
Answers:
sin = -5/13tan = 5/12csc = -13/5sec = -13/12cot = 12/5=============================================
Explanation:
The angle theta is between pi and 3pi/2, excluding both endpoints.
This places theta in the third quadrant (Q3) between 180 degrees and 270 degrees. The third quadrant is in the southwest.
Plot point A at the origin. 12 units to the left of this point, will be point B. So B is at (-12,0). Then five units lower is point C at (-12,-5). Refer to the diagram below. Notice how triangle ABC is a right triangle.
The angle theta will be the angle BAC, or simply angle A.
Since cos(theta) = -12/13, this indicates that
AB = -12 = adjacent
AC = 13 = hypotenuse
Technically, AB is should be positive, but I'm making it negative so that we can then say
cos(angle) = adjacent/hypotenuse
cos(theta) = AB/AC
cos(theta) = -12/13
------------------
If you apply the pythagorean theorem, you should find that BC = 5, which I'll make negative since we're below the x axis. Then we can say
sin(theta) = opposite/hypotenuse
sin(theta) = BC/AC
sin(theta) = -5/13
------------------
If you divide sine over cosine, then you'll get 5/12. The 13's cancel out. This is the value of tangent.
Or you could say
tan(theta) = opposite/adjacent
tan(theta) = BC/AB
tan(theta) = (-5)/(-12)
tan(theta) = 5/12
------------------
To find csc, aka cosecant, you apply the reciprocal to sine
sin = -5/13 which means csc = -13/5
sec, or secant, is the reciprocal of cosine
cos = -12/13 leads to sec = -13/12
and finally cotangent (cot) is the reciprocal of tangent
tan = 5/12 leads to cot = 12/5
------------------
Note: everything but tan and cot is negative in Q3.
Describe how the graph of y = |x - 2| - 5 is a transformation of the graph of y = |x|. Use terms such as "shifted", "reflected", "stretched", or "compressed".
Answers
Answer:
The original graph was shifted 2 units to the left and 5 units down.
Step-by-step explanation:
y = |x|
From this, we go to: y = |x - 2|.
When we want to shift a function f(x) a units to the left, we find f(x - a). So first, the graph was shifted 2 units to the left.
y = |x - 2|.
From this, we go to: y = |x - 2| - 5.
Shifting a function f(x) down b units is the same as finding f(x) - b, so the second transformation was shifting the graph 5 units down.
simplify 6 x + 3y /3
Answers
Answer:
6x + y
Step-by-step explanation:
6x + 3y/3
6x + y
Answer:
6x + y
Step-by-step explanation:
6x + 3y / 3
cancel 3y by 3
6x + y
Consumers Energy states that the average electric bill across the state is $39.09. You want to test the claim that the average bill amount is actually different from $39.09. What are the appropriate hypotheses for this test
Answers
The null hypothesis is [tex]\mu = 39.09[/tex]
The symbol [tex]\mu[/tex] is the Greek letter mu
The alternate hypothesis is [tex]\mu \ne 39.09[/tex] telling us we have a two-tailed test here. The "not equal" is directly tied to the keyword "different" given in the instructions. In other words, mu being different from 39.09 directly leads to [tex]\mu \ne 39.09[/tex]
So either mu is 39.09 or it's not 39.09
You can use H0 and H1 to represent the null and alternate hypotheses respectively.
----------------------
Summary:
The two hypotheses are
H0: [tex]\mu = 39.09[/tex]
H1: [tex]\mu \ne 39.09[/tex]
This is a two tailed test.
x²-7x+5 in the form (x-a)²-b
Answers
Answer:
( x - 3.5)² - 29/4
Step-by-step explanation:
Given :-
x² - 7x + 5Writing in ( x - a)² - b form ,
x² - 7x + 5 x² - 7 * 2/2 * x + 5 x² - (7/2) * 2 * x + 5 x² - (7/2)*2*x +(7/2)²-(7/2)²+5( x - 7/2)² + 5 - 49/4( x - 7/2)² + ( 20-49)/4( x - 3.5)² - 29/4Multiply the polynomial 4x(2x+3) (show work pls)
Answers
Answer:
8^2+12x
Step-by-step explanation:
4x(2x+3)
=4x times 2x+4x times 3
=4 times 2xx+4 times 3x
Answer:
8x^2 +12x
Step-by-step explanation:
Step 1) Multiply each term in the parentheses by 4x
4xx2x+4xx3
Step 2) Calcuate the product
8x^2 +12x
HELPPP PLEASEEE! I tried everything from adding to dividing, subtracting, multiplying but still no correct answer. Can someone help me out here please? I am not sure where to start either now. Thank you for your time.
Answers
What is 35 degrees Celsius in Fahrenheit equal
Answers
Answer:
95°Fahrenheit
hipe this helps you
when a number is added to 1/5 of itself, the result is 24. the equation that models this problem is n+1/5n=24. what is the value of n?
Answers
1
5
n
=
24
⇒
5
n
+
n
5
=
24
⇒
6
5
n
=
24
⇒
n
=
24
×
5
6
⇒
n
=
20
The endpoints of PC are P(4, 1) and Q(4,8). Find the midpoint of PQ
A. (4, 4.5)
B. (0, -3.5)
C. (4.5, 4)
D. (6, 3.5)
Answers
Answer:
A. (4,4.5)
Step-by-step explanation:
Midpoint={x1+x2/2,y1+y2/2}
M={4+4/2,1+8/2}
M={8/2,9/2}
M={4,4.5}
Due to a sale at Macy's you only have to pay 2/3 of the original price of a blouse. your price AFTER the discount $120. What was the original price? Explain how you arrived at this answer.
Answers
9514 1404 393
Answer:
$180
Step-by-step explanation:
The relationship between the prices is said to be ...
(amount you pay) = 2/3 × (original price)
To find the original price, multiply the equation by the reciprocal of the coefficient of the (original price).
(3/2)×(amount you pay) = (3/2)(2/3)(original price) = (original price)
(3/2)×$120 = original price = $180
a car travels 10 km southeast and 15 km in a direction 60 degrees north of east. find the magnitude and direction
Answers
Answer:
the car travels 10km then 15km 60* north of east
Step-by-step explanation:
The time between surface finish problems in a galvanizing process is exponentially distributed with a mean of 41 hours. A single plant operates three galvanizing lines that are assumed to operate independently. Round your answers to four decimal places (e.g. 98.7654).
(a) What is the probability that none of the lines experiences a surface finish problem in 41 hours of operation?
(b) What is the probability that all three lines experience a surface finish problem between 24 and 41 hours of operation?
Answers
Answer:
a) The probability that none of the lines experiences a surface finish problem in 41 hours of operation is 0.0498.
b)The probability that all three lines experience a surface finish problem between 24 and 41 hours of operation is 0.0346.
Step-by-step explanation:
[tex]Mean = \frac{1}{\lambda} = 41\\P(X\leq x)= 1-e^{-\lambda x}[/tex]
[tex]P(X>x)= e^{-\lambda x}[/tex]
a)
[tex]P(x> 41, y>41, Z>41) = (P(X>41))^{3}\\\\P(X>41)=e^{^{-\frac{41}{41}}}=e^{-1}[/tex]
[tex]P(x> 41, y>41, Z>41) = \left (e^{-1} \right )^{3}\\\\P(x> 41, y>41, Z>41) = e^{-3} = 0.0498.[/tex]
b)
[tex]\lambda =\frac{24}{41}\\P(X=1)=e^{-\lambda }\cdot \lambda =\left ( e^{-0.585} \right )\left ( 0.585 \right )\\P(X=1)=0.326[/tex]
For 3 where, P(X=1, Y==1, Z=1)
[tex]= (0.326)^{3} \\\\= 0.0346[/tex]
