Which graph represents the solution set of the system of inequalities?
x+y<1
2y≥x−4
I think its the one in the top right corner (the highlighted one)
Answers
x + y = 1
2y = x - 4
The values of x and y from the system of linear equation are 2 and -1. This means that the intersection of the lines should be at point (2, -1).
Substitute 3 to x and determine the value of y from the second inequality.
2y ≥ x - 4
Substituting,
2y ≥ 3 - 4, y ≥ -1/2
Hence, the solution to this item should be the fourth one.
Related Questions
The african bush elephant weighs between 4.4 tons and 7.7 tons. What are its least and greatest wieghts rounded to the nearest ton
Answers
7.7=8 tons rounded
7.7 rounds to i
How is an emulsion different from a solution?
:The components are mixed unevenly instead of evenly within the emulsion.
:Insoluble instead of soluble particles are suspended within the emulsion.
:Two liquids that normally are not mixable are mixed in the emulsion.
:The components of an emulsion are single elements or compounds instead of a mixture of compounds.
Answers
A new truck that sells for $25,000 depreciates (decreases in value) 11% each year. What will be the value of the truck in 2 years
Answers
Depreciation rate = 11%
Note that 1 - 0.11 = 0.89.
Value after 1 year = $25,000 (0.89) = $22,250
Value after 2 years = $22,250 (0.89) = $19,802.50
Answer: $19,802.50
Answer:
Price of Truck after 2 year = $ 19802.50
Step-by-step explanation:
Given: Price of truck = $ 25,000
Price depreciate at rate of 11% in a year
To find: Price of truck after 2 years
If we let Price of truck to be P = $ 25000
And Rate of deprecation to be R = 11%
And time to be n = 2
now by using formula of deprecation, we get
[tex]A=P\times(1-\frac{R}{100})^n[/tex]
[tex]A=25000\times(1-\frac{11}{100})^2[/tex]
[tex]A=25000\times0.7921[/tex]
A = $ 19802.50
Therefore, Price of Truck after 2 year = $ 19802.50
A scatterplot is produced to compare the size of a lake to the number of fish that are in it. There are 15 data points, each representing a different lake. The points are widely dispersed on the scatterplot with no pattern of grouping. Interpret what the results of the scatterplot tell you about the relationship between the two variables.
Answers
Answer:
Since there is no cluster formed in the scatterplot, the two variables are not related. Therefore, based on the data shown in the scatterplot, the number of fish in a lake is not dependent on the size of the lake.
Step-by-step explanation:
Deidre is 5 feet 4 inches tall and her weight is 135 pounds. her bmi is closest to _____ kg/m2.
Answers
1. Multiply the weight by .45:
135 X .45 = 60.75kg
2. Multiply the height in INCHES by .025
Convert 5feet 4inches to only inches (5*12+4) = 64 inches
Now multiply 64 X .025 = 1.6 m
3. Square the answer from the above step.
1.6 X 1.6 = 2.56m
4. Divide the answer from the first step by the answer from the third step.
60.75kg/2.56m = 23.73.
Deidre bmi is 23.73.
A rectangular picture frame measures 83 cm by 42 cm What is the perimeter or distance around the picture frame in meters
Answers
[tex]P=2w+2l[/tex]
We can find our answer by direct substitution of known values:
[tex]P=2(83cm)+2(42cm)[/tex]
[tex]P=166cm+84cm[/tex]
[tex]P=250cm[/tex]
We can then convert to meters:
[tex]250cm * \frac{1m}{100cm} = 0.25m[/tex]
The perimeter of the picture frame is 0.25m.
Sharon needs 64 credits to graduate from her community college. So far she has earned 24 credits. What percent of the required credits does she have?
Answers
A percentage is a number or ratio expressed as a fraction [tex]100[/tex]. Hence, Sharon has [tex]12.5[/tex]% of the credits required.
What is the percentage?
A percentage is a number or ratio expressed as a fraction [tex]100[/tex]. It is often denoted using the percent sign, "%".
Here given information:-
Sharon needs [tex]64[/tex] credits and he earned [tex]24[/tex] credits.
So,
[tex](\frac{24}{64})[/tex]×[tex]100[/tex][tex]=\frac{1}{8}[/tex]×[tex]100[/tex]
[tex]=0.125[/tex]×[tex]100[/tex]
[tex]=12.5[/tex]%
Hence, Sharon has [tex]12.5[/tex]% of the credits required.
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Six students measure the acceleration (in meters per second per second) of an object in free fall. The measured values are: 10.56, 9.52, 9.73, 9.80, 9.78, 10.91.The students want to state that the absolute deviation of each measured value xfrom the mean is at most
d. Find the value of
d.
Answers
x = [10.56, 9.52, 9.73, 9.80, 9.78, 10.91]
There are 6 measurements.
Calculate the mean.
m = (10.56+9.52+9.73+9.80+9.78+10.91)/6 = 10.05
Calculate deviations from the mean.
y = |x - m|
= [0.51, 0.53, 0.32, 0.25, 0.27, 0.86]
The greatest deviation from the mean is d = 0.86.
Calculate the average absolute deviation.
(0.51+0.53+0.32+0.25+0.27+0.86)/6 = 0.4567
Answer:
d = 0.86
Jenny earned a 77 on her most recent test. Jenny’s score is no less than 5 points greater than 4/5 of Terrance’s score. If t represents Terrance’s score, which inequality represents the situation?
Answers
Answer:
The situation is represented by the following inequality :
[tex]\bf 77\geq \frac{4}{5}\cdot t+ 5[/tex]
Step-by-step explanation:
Score earned by Jenny on her most recent test = 77
Let the Terrance's score is represented by t
[tex]\frac{4}{5}\text{ of the Terrance's score is = }\frac{4}{5}\cdot t[/tex]
If Terrance's score is 5 points greater then the points earned by Terrance's in the test is represented by :
[tex]\bf\frac{4}{5}\cdot t+ 5.......(1)[/tex]
Now, according to the given condition in the question , Jenny's score is not less than the score represented by (1)
⇒ Jenny's score is greater than equal to the score represented by (1)
Hence, The situation is represented by the following inequality :
[tex]\bf 77\geq \frac{4}{5}\cdot t+ 5[/tex]
Answer:
B
Step-by-step explanation:
based on the pattern of the drawings which conjecture is reasonable to make?
A. when a pair of parallel lines is intersected by a third line, the corresponding angles are complementary
B. when a pair of parallel lines is intersected by a third line, all of the angles formed are congruent.
C. when a pair of parallel lines is intersected by a third line, the corresponding angles are congruent
D. when a pair of parallel lines is intersected by a third line, the corresponding angles are supplementary.
Answers
the 2 angles in each picture are the same - meaning they are congruent,
so the answer is:
C. when a pair of parallel lines is intersected by a third line, the corresponding angles are congruent
Conjectures are simply opinions from a given information.
The conjecture that can be formed is: C. when a pair of parallel lines is intersected by a third line, the corresponding angles are congruent
From the three diagrams, we can see that:
[tex]\mathbf{30^o = 30^o}[/tex][tex]\mathbf{35^o = 35^o}[/tex][tex]\mathbf{50^o = 50^o}[/tex]From the figures above, we have the following observations
The angles are congruentThe angles are correspondingThe congruence of the angles is based on parallel lines, intersected by a third line (i.e. the transversal)Hence, the conjecture that can be formed is: option (c)
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Find the sum of a 9-term geometric sequence when the first term is 4 and the last term is 1,024 and select the correct answer below.
A.682
B.2044
C.2048
D.678
Answers
Answer: The correct option is (B) 2044.
Step-by-step explanation: We are given to find the sum of a 9-term geometric sequence when the first term is 4 and the last term is 1,024.
We know that
the n-th term of a geometric sequence with first term a and common ratio r is given by
[tex]a_n=ar^{n-1}.[/tex]
According to the given information, we have
[tex]a=4[/tex]
and
[tex]ar^{9-1}=1024\\\\\Rightarrow 4\times r^8=1024\\\\\Rightarrow r^8=\dfrac{1024}{4}\\\\\Rightarrow r^8=256\\\\\Rightarrow r^8=2^8\\\\\Rightarrow r=2.[/tex]
Therefore, the sum of the 9-term geometric sequence is given by
[tex]S_9\\\\\\=\dfrac{a(r^9-1)}{r-1}\\\\\\=\dfrac{4\times(2^9-1)}{2-1}\\\\\\=\dfrac{4\times(512-1)}{1}\\\\=4\times511\\\\=2044.[/tex]
Thus, the required sum of the 9-term sequence is 2044.
Option (B) is CORRECT.
a pyramid with a square base of length 3cm and height 16cm
Answers
s = 16.0702 cm
a = 3 cm
e = 16.14 cm
r = 1.5 cm
V = 48 cm3
L = 96.421 cm2
B = 9 cm2
A = 105.421 cm2
The volume of a square pyramid:V = (1/3)a2hSlant Height of a square pyramid:By the Pythagorean theorem, we know thats2 = r2 + h2since r = a/2s2 = (1/4)a2 + h2, ands = √(h2 + (1/4)a2)This is also the height of a triangle sideLateral Surface Area of a square pyramid (4 isosceles triangles):For the isosceles triangle Area = (1/2)Base x Height. Our base is side length a, and for this calculation our height for the triangle is slant height s. With four
sides we need to multiply by 4.L = 4 x (1/2)as = 2as = 2a√(h2 + (1/4)a2)Squaring the 2 to get it back inside the radical,L = a√(a2 + 4h2)Base Surface Area of a square pyramid (square):B = a2Total Surface Area of a square pyramid:A = L + B = a2 + a√(a2 + 4h2))A = a(a + √(a2 + 4h2))
The domain for f(x) and g(x) is the set of all real numbers. Let f(x) = 2x2 + x − 3 and g(x) = x − 1. Find f(x) • g(x).
A. 2x3 − x2 + 4x − 3
B. x2 − 4x + 3
C. 2x3 − x2 − 4x + 3
D. 2x3 − 4x2 + 3
Answers
so the answer should be C
14-3x=4x solve and explain
Answers
Flip
4x = 14 - 3x
Add both sides by 3x
7x = 14
Divide both sides by 7
x = 2
Have an awesome day! :)
in 2003, a gallon of gas cost $1.75. In 2013 a gallon of gas cost $3.25. Write an equation to model this situation.
Answers
To model the situation of the gas prices in 2003 and 2013, we can use a linear equation. The equation to model this situation is y = $0.15x - $298.70.
Explanation:To model the situation of the gas prices in 2003 and 2013, we can use the equation of a linear relationship between the year (x) and the cost of gas (y). We can use the formula y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope (m):
The change in cost of gas is $3.25 - $1.75 = $1.50The change in years is 2013 - 2003 = 10Therefore, the slope (m) is $1.50 / 10 = $0.15.
Next, let's find the y-intercept (b):
Using the point (2003, $1.75), we can substitute the values into the equation and solve for b:$1.75 = $0.15(2003) + b
b = $1.75 - $0.15(2003)
b = $1.75 - $300.45
b = -$298.70
Therefore, the equation to model this situation is y = $0.15x - $298.70, where x is the year and y is the cost of gas.
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2.What is the correct equation of the line shown below ?
Answers
Since the line enters the y-axis at (0,3) the y-intercept of the equation would be 3 (as according to the y=mx+b format where b is the y-intercept and m is the slope). The slope would be 3/2 since when you find two perfect points (I used (0,3) and (2,6)) and you use the rise over run method (move up 3 from (0,3) and 2 to the right to get to (2,6)), your slope is 3/2.
The equation of the line shown is y = (3/2)x + 3.
What is the equation of line?The general equation of a straight line is
y = mx + c,
where m is the gradient or slope, and
y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
Now given points from the line passes are (0,3) and (-4,-3)
Therefore we have,
x₁ = 0
y₁ = 3
x₂ = -4
y₂ = -3
Now since the slope of the line is given as,
m = (y₂ - y₁)/(x₂ - x₁)
⇒ m = (-3 - 3)/ (-4-0)
⇒ m = -6/(-4)
⇒ m = 6/4
or, ⇒ m = 3/2
Now, for intercept c we can put any of points in the equation of line.
So, put (0,3)in the equation of line
3 = m(0) + c
3 = 0 + c
⇒ c = 3
Hence the required equation of line is given as,
y = mx + c
put the values of m and c,
y = (3/2)x + 3
which is the required equation of the line shown
Hence,the equation of the line shown is y = (3/2)x + 3.
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Write the next two terms in the pattern. 3, 10, 17, 24, . . .
Answers
So next values would be 31 and 38
10-3 =7
each term increases by 7
so 24 +7 = 31
31+7 = 38
next 2 terms are 31 & 38
PLEASE HELP
Solve for x.
−32>−5+9x
Enter your answer, as an inequality, in the box.
Answers
-32 + 5 < 9x
-27 < 9x
-3 < x
x > -3
hope that helps, God bless!
Inequality is a statement of an ordered relationship
The value of x as inequality is less than -3.
x < -3 is our answer.
What is inequality?It is a statement of an ordered relationship
- greater than,
- greater than or equal to,
- less than,
- less than or equal to between two numbers or algebraic expressions.
Example:
x > 3
y < 5
x ≤ 6
y ≥ 2
We have,
-32 > -5 + 9x
Add 5 on both sides.
-32 + 5 > -5 + 9x + 5
[ -32 + 5 = -27 ]
-27 > 9x
Divide both sides by 9.
-27/9 > 9x/9
-9 x 3 / 9 > 9x / 9
-3 > x
This can be written as:
x < -3
Thus,
The value of x as inequality is less than -3.
i.e x < -3
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Which transformation is not isometric?
Answers
Ronald walks from home to Taco Bell to eat everyday. It takes him 30 minutes to walk the 2 mile distance. A) write a function for Ronald’s wall. Let x be the number of minutes he walks.
B) what should the domain of the function be?
Answers
[tex]d=vt[/tex]
where d[tex]y= \frac{1}{15}x [/tex]= distance,
v = velocity,
t = time
In this case, d = 2 mi., t = 30 min. So we get
[tex]2=30v[/tex]
Dividing both sides by 30, we get
[tex]v= \frac{2}{30}= \frac{1}{15} [/tex]
Thus a function for his walk would be
[tex]y= \frac{1}{15} x[/tex]
where y = distance and x = number of minutes he walks.
b) Domain of a function is a set of x-values on which the function defined. In this case, the number of minutes is 30 at maximum. So the domain of the function is [0, 30].
The relative frequency of a car travelling through a road junction having exactly two occupants is 0.26.If 5,000 cars are observed passing through the junction, how many of the cars could be expected to have only two occupants?
Answers
5000 x 0.26 = ??
What is the average of 5.24,6.875,3.298,5.7,4.98? Round the answer to 2 decimal points
Answers
What is the surface area of a cylinder whose radius is 3 inches and whose height is 10 inches? Round to the nearest tenth.
SA = 2π r2 + 2π rh
A. 226.1 square inches
B. 241.8 square inches
C. 244.9 square inches
D. 543.3 square inches
Answers
8 less than one third of x is y
Answers
I think this is what you were looking for seeing that you cannot solve this problem without an 'x' or 'y'.
Help with math please.
Select the correct rate of change and y -intercept for the linear function that contains the points (4, 6) and (5, 3).
Question 1 options:
The rate of change is –3, and the y -intercept is 18.
The rate of change is 3, and the y -intercept is –6.
The rate of change is 1/3, and the y intercept is 4 2/3
The rate of change is -1/3, and the y intercept is 7 1/3
Answers
The rate of change is the slope (rise/run, y/x). To find that, we use the equation (y2-y1) over (x2-x1). It means take the second "y" and subtract it from the first "y" and the same to "x". If I plug in the numbers, it would be (3-6) over (5-4), and after you subtract, the answer simplifies to: -3/ 1 which is -3. Yay! We got the slope (rate of change) done.
Now let's find the y-intercept by using the formula of point-slope form,
y-y1= m (slope) (x-x1). This is saying you "y" is subtracted from the first
"y" of the points which equals the slope (m) times the quantity of "x" subtracted by the first "x" of the points.
Let's plug the numbers in: y-6 = -3 (x-4). Let's distribute -3 to the parenthesis, and after that it should simplify to: y-6 = -3x + 12. To get "y" by itself, add 6 to both sides: y = -3x +18. We have finally found the slope-intercept equation for those two points (4,6) and (5,3). To then find the y-intercept in this equation, it would be the 18, because -3 is the slope, so that makes 18 the y-intercept.
In conclusion, the rate of change is -3 and the y-intercept is 18.
I hope this helps!
May
Bill Payne visits his local bank to see how long it will take for $1,000 to amount to $1,900 at a simple interest rate of 12 ½%. Provide Bill with the solution to his problem in years. A. 6.5 years B. 7.2 years C. 12.5 years D. 10.2 years
Answers
with an initial starting balance of $1,000.00Balance after 6 years with annual interest of 12.05% $1,979.12
7 years- 2,217.60$
12 years- 3,916.90
Help me i hate word problems
Answers
so the question would be: how many times does fit into 3.5?
if you want to divide by a fraction, you need to multiply by the reverse of it.
so the answer is: 10 servings of lemonade ( and a little bit will be left over for half a serving).
Hope this helps!
Which statement is true about the equations –3x + 4y = 12 and x – y = 1?
The system of the equations has exactly one solution at (–8, 3).
The system of the equations has exactly one solution at (–4, 3).
The system of the equations has no solution; the two lines are parallel.
The system of the equations has an infinite number of solutions represented by either equation.
Answers
Answer:
C
Step-by-step explanation:
Its C just did the test
Find the volume of the composite solid. Round your answer to the nearest hundredth.
A.239.24cm^3
B.246.08cm^3
C.294.03cm^3
D.308.78cm^3
Answers
We can find the total vol. by adding the two together: Vol (v)total = vol (pyra) + vol (box)
vol (tot) = (1/3×base×height) + (l×w×h)
In order to find the height (h) of the triangle, we imagine a string dropped straight down from the apex (tip), which falls perfectly to center of the base of pyramid. Now the distance from the bottom of that string to edge is 1/2×6.7 = 3.35. Use Pythagorean Theorem to determine the pyramid height:
[tex] {5.8}^{2} = {h}^{2} + {3.35}^{2} \\ {h}^{2} = {5.8}^{2} - {3.35}^{2} \\ h \: = \sqrt{({5.8}^{2} - {3.35}^{2})} \\ h = \sqrt{(33.64 - 11.22)} \\ h = \sqrt{22.42} = 4.73 \: cm[/tex]
Now we can solve our volume, so the base of pyra = l×w = 6.2×6.7 = 41.54
vol (tot) = (1/3×base×height) + (l×w×h)
vol = (1/3×41.54×4.73) + (6.7×6.2×5.5)
vol = (65.49) + (228.47) = 293.96
[tex]vol = 294 \: {cm}^{3} > > \: answer \: (c)[/tex]
On average, how many times must a 6-sided die be rolled until a 6 turns up twice in a row?
Answers
Chance of two 6s: (1/6)² = 1/36
The chance of rolling a 6 on 2 dice is 1/6 x 1/6.
1/6 x 1/6 = 1/36.
The average number of times for the first 6 would be 6
I'm not sure how to explain this part
But the average number of times for the second one would be 7.
To get the consecutive number of times, multiply them together:
6 x 7 = 42.
It would take an average of 42 times.
Hope This Helps You!
Good Luck :)
- Hannah ❤