3. (05.06 MC)
Graph the system of Inequalities presented here on your own paper, then use your graph to answer the following questions:
y < 4x – 2
y>5/2x-2 (should be the greater than or equal to sign)
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution area. (6 points)
Part B: Is the point (-2,-2) Included in the solution area for the system? Justify your answer mathematically. (4 points)
(10 points)
9514 1404 393
Answer:
A) The first inequality has a dashed boundary line with a slope of 4 and a y-intercept of -2. The shading is below the line. The second inequality has a solid boundary line with a slope of 5/2 and a y-intercept of -2. The shading is above the line. The solution space is a narrow wedge extending up and to the right of the y-intercepts at (0, -2) through the fourth quadrant into the first quadrant.
B) Not in the solution space. The point does not satisfy y < 4(-2) -2 because -2 is not less than -10.
Step-by-step explanation:
Part A:
The boundary line of each inequality is in slope-intercept form, so can be drawn easily by finding points with the appropriate slope=rise/run from the common y-intercept at (0, -2).
The first inequality does not include the "or equal to" case, so the boundary line will be dashed. The relation of y and the inequality symbol is y < ( ), so the shading will be below the line, where y-values are less than those on the line.
The second inequality includes the "or equal to" case, so the boundary line is solid. The relation of y and the inequality symbol is y ≥ ( ), so the shading will be above the line, where y-values are greater than those on the line.
The two shaded areas overlap in a narrow wedge between lines with slope 2.5 and 4. The lower-left point of the wedge is the common y-intercept at (0, -2). It extends through the fourth quadrant into the first quadrant. This wedge is the solution area.
__
Part B:
Based on the above description, no part of the solution space is in the third quadrant, where the point (-2, -2) lies. The point is not in the solution space. It does not satisfy the first inequality:
[tex]-2\nless(4)(-2)-2=-10[/tex]
In 1965, the population of a country was 192 thousand to 3 significant figures.
In 2020, the population of that country was 366 thousand to 3 significant figures.
Work out the percentage increase in population. Give your answer correct to 2 significant figures.
The percent change in population is 90.65%.
What is percent?A percentage is a figure or ratio that can be stated as a fraction of 100. If we need to calculate the percentage of a number, we must divide it by its full value and then multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".
Given population of country in 1965 = 192 thousand = 1,92,000.
population of country in 2020 = 366 thousand = 3,66,000
the increase in population is = 366000 - 192000 = 1,74,000
the percentage increase = (100)(increase in population)/(1965 population)
the percentage increase = (100) (174000)/(192000)
the percentage increase = 90.625%
Hence the percent increase is 90.62%.
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10,14,18,22,26 find the 12 term of the sequence
Answer:
30,34,38,42,46,50,54,58,62,66,70
HAVE A NICE DAY
WILL GIVE BRAINLST :)
Answer:
A. 103 degrees
B. 77 degrees
C. 60 Degrees
Step-by-step explanation:
A. Triangles' interior angles add up to 180, so if you already have 2 angles you just need to put them together, and subtract them from 180.
47+30=77
180-77=103
B. Lines also are 180, so 103-180=77
C. Interior angles of a triangle add up to 180, so 180/3 is how you get your answer.
Please help me. It would be greatly appreciated
Answer:
11a) x=18
11b) 6x=108
11c) 4x=72
Step-by-step explanation:
11a) A line is equal to 180 degrees. Therefore, 6x and 4x have to add up to be 180.
6x+4x=180
10x=180
x=18
11b) We know what x is so we have to plug x into the expression. 6x=6(18)=108. 6x=108
11c) We know what x is so we have to plug x into the expression 4x=4(18)=72
4x=72.
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Calculate the perimeter of a square with side 12cm
Answer: 48 cm
Step-by-step explanation:
12 + 12 + 12 + 12 = 48
someone plz help :(
i'm struggling heree
Answer:
39.96 in²
Step-by-step explanation:
10.8x3.7=39.96
Answer:
19.98
Step-by-step explanation:
area=½×base ×height
½×10.8×3.7
=19.98
If mBCD = 148°, what is m∠BCD?
74°
32°
148°
106°
Answer:
Option (1)
Step-by-step explanation:
Given : m(arc BCD) = 148°
By the property,
Inscribed angle formed by an arc measures half the measure of the arc.
m(arc BCD) = 2(m∠BCD)
148° == 2(m∠BCD)
m(∠BCD) = 74°
Therefore, Option (1) will be the correct option.
ratiearbiteracy
toen we zui
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Ghics12
The average inflation rates for the period 2016 to 2017 are shown in the following iable.
2017
1 2018
Average Inflation rate 4,51%
6,59%
Cost of a brown bread
R9.99
A
8.1.1
Explain the meaning of the term inflation rate.
8.1.1
Calculate the cost of a loaf of brown bread in 2017 by using the average
inflation rates that are given in the table above.
ON NO: 3
: MAPS AND SCALES
ensure Learners know the following:
IBER/RATIO SCALE
If I earned $15 babysitting, I would deposit (or add) $15 to the previous balance.
If I bought a new sweatshirt for $42.66, I would withdraw (or subtract) $42.66 from the previous balance.
If transferred $100, I would subtract $100 from the account it is leaving and add $100 to the account it is going to.
Answer:
57 dollars and 66 cents will be subtracted from the depositeand get the answer of 157.66
Step-by-step explanation:
Relay Race Results
10. The table shows the time each
member of two relay teams took
to complete her leg of a relay race.
Team II won the race by 2 s. How
many seconds did Trina take to
run her leg of the race?
Leg
1
Team 1
Name
Time (s)
Ali
22
Bryn 25
Mai
23
Team II
Name
Time (s)
Lea
23
Niki
22
Trina
2
3
4
Tara
21
Sara
20
93
because if the team second wones the match with two points then the answer will be 93
Help ME WITH THIS QUESTION THANKS !
Answer:
6 units
Step-by-step explanation:
9x - 4 = 2 ( 5x - 5 )
9x - 4 = 10x - 10
10x - 10 = 9x - 4
10x - 9x = - 4 + 10
x = 6
Is it true that congruent figures have the same shape and the same size?
TRUE OR FALSE?
22 POINTS BTW!!
Answer:
yahh
Step-by-step explanation:
thats true
i know its help
Answer:
True
Step-by-step explanation:
Two congruent figures have the same shape and size.
The sum of two numbers is -3, and their difference is 25. Find the numbers.
The ratio of sweaters to dresses that Susan has is 7:2. If Susan has 14 dresses then how many sweaters does she have?
Answer:
4 sweaters
Step-by-step explanation:
If the ratio is 7:2, then 14//7 = 2
2x2=4
A social scientist would like to analyze the relationship between educational attainment (in years of higher education) and annual salary (in $1,000s). He collects data on 20 individuals. A portion of the data is as follows:
Salary Education
34 3
66 1
89 4
56 3
71 7
80 2
111 7
51 0
23 7
36 2
100 1
35 1
71 6
68 9
163 5
56 0
86 5
58 4
128 9
33 0
Salary Education
34 3
66 1
⋮ ⋮
33 0
a. Find the sample regression equation for the model: Salary = β0 + β1Education + ε. (Round answers to 2 decimal places.) Salaryˆ= + Education
b. Interpret the coefficient for Education.
As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $4,690.
As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $4,690.
As Education increases by 1 unit, an individual’s annual salary is predicted to decrease by $8,590.
As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $8,590.
c. What is the predicted salary for an individual who completed 7 years of higher education? (Round coefficient estimates to at least 4 decimal places and final answer to the nearest whole number.)
Salaryˆ $
Answer:
y = 4.69X + 52.93 ;
As Education increases by 1 unit, an individual’s annual salary is predicted to increase by $4,690. ;
$86000
Step-by-step explanation:
Given the data:
X:
34
66
89
56
71
80
111
51
23
36
100
35
71
68
163
56
86
58
128
33
Y:
3
1
4
3
7
2
7
0
7
2
1
1
6
9
5
0
5
4
9
0
The regression equation obtained using a linear regression calculator :
y = 4.689X + 52.93182
Where ;
y = Salary ; x = Educational attainment
Slope is the Coefficient of x = 4.689
Intercept = 52.93
The slope value in thousand = 4.689 * 1000 = 4689 = 4690 (the slope is interpreted to the mean the change in y value per unit change in the value of x)
Therefore, salary increases by about $4690 for every unit increase.
If x = 7
y = 4.689(7) + 52.93182
y = 32.823 + 52.93182
y = 85.7548
Salary =, $86,000
Five more than a number is greater than 26
NEED HELP NOW!
Question 4(Multiple Choice Worth 5 points) (07.06A MC) What is the initial value of the function represented by this table?
The proportional relationship between the
number of inches a candle has burned away, b, at
any time in hours, t, can be represented by the
equation b = 0.75t. At what rate does the
candle burn, in inches per hour?
Candles should burn one hour for every 1 inch in diameter of the actual candle size. For example, a candle that is 2 inches across should burn for 2 hours.
At what rate does then candle burn, in inches per hour?
Smaller candles with smaller wicks will burn at a rate of 7 to 9 hours per 28 g of wax used. Larger candles with larger wicks consume wax at a faster rate. The larger wicks can be expected to yield 5 to 7 hours per 28 g of wax used.
Estimate the total number of burns by dividing the total wax weight used in the candle (not the weight of the candle with container) by the amount of wax used from burning the candle. Finally, multiply the estimated total burns by the burn time hours. This will provide an estimate of the candle's burn time.
The two main factors for burning candles is wick size and type of wax. Wider or thicker wicks will burn much faster than thin ones, and the material the wick is made with can also make an impact. Different types of candle wax burn at different temperatures.
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Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. The area of a cross section perpendicular to the base of a rectangular prism is 45 square inches. If the length and width of the base are 5 inches each, what is the height of the prism? The height of the prism is __ inches.
Answer:
i think it 20 if im wrong im sorry
The height of the prism is 9 inches if the area of a cross-section perpendicular to the base of a rectangular prism is 45 square inches.
What is a rectangular prism?It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape. It is also called a cuboid.
Please refer to the attached picture for the figure:
We have:
The area of a cross-section perpendicular to the base of a rectangular prism is 45 square inches.
As we know the area of the rectangular face = lengthxwidth
From the figure:
The area of the rectangular face = hx5
h is the height of the rectangular prism.
45 = hx5
h = 45/5
h = 9 inches
Thus, the height of the prism is 9 inches if the area of a cross-section perpendicular to the base of a rectangular prism is 45 square inches.
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Someone answer this please
Answer:
[tex] 1,334.5 \: {cm}^{3} [/tex]
Step-by-step explanation:
Height of the cylinder h = 17 cm
Radius of the cylinder r = 5 cm
[tex]V_{cylinder} = \pi {r}^{2} h \\ \\ = 3.14 \times {(5)}^{2} \times 17 \\ \\ = 3.14 \times 25 \times 17 \\ \\V_{cylinder} = 1,334.5 \: {cm}^{3} [/tex]
what fraction is 40 minutes of 8 hours
40 minutes of 8 hours as a fraction is 1/12.
What is fraction?Fractions represent the parts of a whole or collection of objects. A fraction has two parts namely numerator (upper part) and denominator (lower part).
Given are 40 minutes to 8 hours.
We can write -
(40 minutes/8 hours)
{40 minutes/(8 x 60)}
(40/480)
1/12
Therefore, 40 minutes of 8 hours as a fraction is 1/12.
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Given that the value of m+n=-2, find the value of 4m+4n-3.
Answer:
-11
Step-by-step explanation:
m + n = - 2
4(m + n) = - 2(4) (multiplying both sides by 4)
4m + 4n = - 8
4m + 4n - 3 = - 8 - 3 (Subtracting 3 from both sides)
4m + 4n - 3 = - 11
[tex]if \: x = 1 - \sin( \alpha ) \: and \: y = 1 + \cos( \alpha ) \\ [/tex]
Express y in terms of x and alpha only
Answer:
A sample of helium was compressed at 35 °C from a volume of 0.5 L
to 0.25 L where the pressure is 500 mmHg. What was the original pressure?
Step-by-step explanation:
Find the equation of the straight line passing through the point (3, 5)
which is perpendicular to the line
y = 3x + 2
Answer:
y = -1/3x + 6
Step-by-step explanation:
the slope is -1/3 because you find the the reciprocal and switch the sign. To find the y intercept you plug in the points to the equation.
5 = -1/3(3) + b
5 = -1 + b
6 = b
Me jay bought a television for 9560, he used it for some years and later sold it at a profit of 1439. Find his selling price
Answer:
10999
Step-by-step explanation:
9560 + 1439 = 10999
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Write a fraction that is equivalent to 5/6
Answer:
10/12 , 15/18 , 20/24 ...etc
9+2+4+6+123=?
please help
Answer:
144
Step-by-step explanation:
9+2+4+6+123=
11+10+123
21+123
144
Khan Academy math question
Answer:
the answer is 0 you're welcome bye
Point R on the coordinate grid below shows the location of a car in a parking lot. A second car needs to park 7 units above R to leave room for a utility truck. What are the coordinates of the location of the second car?
Image of a coordinate grid with point R located at 2, negative 4.
(−5, −4)
(−5, 3)
(2, −3)
(2, 3)