Graph the solution set of the following linear inequality:2y < 2x + 4AnswerKeypadKeyboard ShortcutsThe line will be drawn once all required data is provided and will update whenever a value is updated. Theregions will be added once the line is drawn.101Choose the type of boundary line:Dashed -O Solid (-) O--)5Enter two points on the boundary line:10--5310Select the region you wish to be shaded:5ОАOB19
Answers
Explanation
[tex]2y<2x+4[/tex]
To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.
Step 1
a)isolate y in the inequality
[tex]\begin{gathered} 2y<2x+4 \\ \text{divide both sides by 2} \\ \frac{2y}{2}<\frac{2x+4}{2} \\ y=\frac{2x+4}{2}=\frac{2x}{2}+\frac{4}{2} \\ y=x+2\Rightarrow\text{ Line} \end{gathered}[/tex]Step 2
draw the line:to do that we need 2 points from the line
a) for x=0
[tex]\begin{gathered} y=x+2 \\ \text{replace} \\ y=0+2=2 \\ \text{hence} \\ \text{Point 1(0,2)} \end{gathered}[/tex]b)for x= 3
[tex]\begin{gathered} y=x+2 \\ \text{replace} \\ y=3+2=5 \\ \text{hence} \\ \text{Point 1(3,5)} \end{gathered}[/tex]c) draw a dotted line that passes trought point 1( 0,2) and point 2 (3,5)
d) as we are searching for the y values smaler thatn the function
[tex]ywe need to take the area under the linetherefore, the answer is
Related Questions
What are the potential solutions to the equation below?
2ln(x+3)=0
X=-3 and X=-4
X=-2 and x=-4
X= 2 and X=-3
X= 2 and X-4
Answers
2In(x+3) = 0
This is the same as:
[tex]In(x+3)^2=0[/tex]Take the exponent of both-side
[tex]e^{In}(x+3)^2=e^0[/tex][tex](x+3)^2=1[/tex]Take the square root of both-side
[tex]x+3=\pm1[/tex]subtract 3 from both-side
x = ± 1 - 3
Either x = -1 - 3 or x = +1 - 3
x = -4 or x = -2
If a, b and c represent the side lengths of a triangle and √2(a + b) = √a+c+ √a-c what type of triangle is it?
Answers
Given:
The given expression is
[tex]\sqrt{2(a+b)}=\sqrt{a+c}+\sqrt{a-c}[/tex]Required:
We want to find the type of triangle
Explanation:
First take square both side
[tex]\begin{gathered} \sqrt{2(a+b)}=\sqrt{a+c}+\sqrt{a-c} \\ 2a+2b=a+c+2\sqrt{a^2-c^2}+a-c \\ 2b=2\sqrt{a^2-c^2} \\ b=\sqrt{a^2-c^2} \end{gathered}[/tex]now again take square for both side
[tex]\begin{gathered} b^2=a^2-c^2 \\ a^2=b^2+c^2 \end{gathered}[/tex]Final answer:
Right angle triangle
what is the volume in cubic inches of the candle
Answers
1) The volume of a cylinder is given by a formula. This one down here:
[tex]V=\pi\cdot r^2\cdot h[/tex]2) Note that the Diameter is twice the radius, therefore it is safe to say that the radius is 1.5"
3) So we can plug these data into the formula this way:
[tex]\begin{gathered} V=\pi\cdot(1.5)^2\cdot3 \\ V=\pi\cdot2.25\cdot3 \\ V=3.14\cdot2.25\cdot3 \\ V=21.2057\ldots \\ V\approx21in^{3} \end{gathered}[/tex]Irene earned a commission of $5130 on sales of $90,000. What rate of commission was she paid? (Be sure to include the % symbol in your answer.)
Answers
We will have that $90000 is the total of sales and therefore the 100%, then we want to know the percentage that $5130 represents:
[tex]p=\frac{5130\cdot100}{90000}\Rightarrow p=5.7[/tex]She's getting a commission at a rate of 5.7%.
Malcolm is driving 1, 373 miles from Wichita to Charleston for a family reunion. He drives 468 miles the first day and 434miles the second day. Round each distance to the nearest ten and estimate about how many miles Malcolm has left to drive.
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This problem describes two parts of a trip, on the first day the trip was 468 miles long, and on the second day, it was 434 miles long. We need to calculate how far from the destination the driver is from their destiny after the second day, knowing that the whole trip is 1373 miles long.
The first step we need to take, is to round the distances for each day to the nearest ten, this is done below:
[tex]\begin{gathered} \text{ day 1}\cong470\text{ miles} \\ \text{ day 2}\cong430\text{ miles} \end{gathered}[/tex]Now we need to subtract the distances for each day from the total distance:
[tex]\begin{gathered} \text{ distance left}\cong1373-470-430 \\ \text{ distance left}\cong473 \end{gathered}[/tex]The driver needs to drive approximately 470 miles to complete the trip.
Ngraph?108+fog64Of(-3) = 94O f(-4) = gOf(-3) = g(Of(-4) = 962++B-4-3-2-12+ 1 2 3 4 5 6 x-6--8EL-10NO-120
Answers
Intersection of Lines
The image shows two lines, f(x) in blue and g(x) in red.
The lines intercept at one point (-3, -4).
This means that f(-3) = -4 and g(-3) = -4, therefore:
f(-3) = g(-3)
17a - 13ab + 4a - 2b + 4ab
Answers
Answer
21a - 9ab - 2b
Step-by-step Explanation
The question wants us to simplify the expression given
17a - 13ab + 4a - 2b + 4ab
The first step is to collect like terms and bring the terms with the same coefficient together
17a - 13ab + 4a - 2b + 4ab
= 17a + 4a - 13ab + 4ab - 2b
= 21a - 9ab - 2b
This cannot be simplified further. So, the simplified solution is
21a - 9ab - 2b
Hope this Helps!!!
Question 9 (5 points)(02.05 LC)Solve the inequality 2x + 8 < 5x - 4. (5 points)a x > 4 b x > 1 c x < 1 d x < 4
Answers
Given:
2x + 8 < 5x - 4.
Required:
To tell which option is correct
Explanation:
First of all rearrange the equation and subtract what is on rigjt side we get
2x+8-(5x-4)<0
pull out like factors
-3x+12=-3(x-4)
divide both side by 3
remember to flip the inequality sign
solve basic inequality and we get
x>4
Require
5 -x - 4y + 5z = -21 13) -3a - b - 3c = -8 -5a + 3b + 6c = -4 -6a - 4b +c= -20 14) -5x + 3y + 6z=4 -3x + y + 5z = -5 -4x +2y+z=17
Answers
To solve the system of equations:
[tex]\begin{gathered} -3a-b-3c=-8 \\ -5a+3b+6c=-4 \\ -6a-4b+c=-20 \end{gathered}[/tex]by elimination we choose two equations and eliminate one of the variables. Choosing the first two equations and multiplying the first one by 2 we have:
[tex]\begin{gathered} -6a-2b-6c=-16 \\ -5a+3b+6c=-4 \end{gathered}[/tex]if we add the equation we get:
[tex]-11a+b=-20[/tex]Now, from the original system we choose the second and third equations and multyply the third by -6, then we have:
[tex]\begin{gathered} -5a+3b+6c=-4 \\ 36a+24b-6c=120 \end{gathered}[/tex]Adding the two equations we have:
[tex]31a+27b=116[/tex]Now that we eliminate the same variable from two sets of equations we have the new system:
[tex]\begin{gathered} -11a+b=-20 \\ 31a+27b=116 \end{gathered}[/tex]To solve this sytem we mutiply the first equation by -27, then we have:
[tex]\begin{gathered} 297a-27b=540 \\ 31a+27b=116 \end{gathered}[/tex]adding this equation we have:
[tex]\begin{gathered} 328a=656 \\ a=\frac{656}{328} \\ a=2 \end{gathered}[/tex]Once we have the value of a we plug it in the equation
[tex]-11a+b=-20[/tex]to find b:
[tex]\begin{gathered} -11(2)+b=-20 \\ -22+b=-20 \\ b=22-20 \\ b=2 \end{gathered}[/tex]Now that we have the values of a and b we plug them in the equation
[tex]-3a-b-3c=-8[/tex]to find c:
[tex]\begin{gathered} -3(2)-2-3c=-8 \\ -6-2-3c=-8 \\ -8-3c=-8 \\ 3c=-8+8 \\ 3c=0 \\ c=\frac{0}{3} \\ c=0 \end{gathered}[/tex]Therefore the solution of the system is:
[tex]\begin{gathered} a=2 \\ b=2 \\ c=0 \end{gathered}[/tex]Can you please help me solve the step by step7(x-6)=-14
Answers
we have the equation
7(x-6)=-14
solve for x
that means -----> isolate the variable x
step 1
Divide both sides by 7
7(x-6)/7=-14/7
simplify
x-6=-2
step 2
Adds 6 both sides
x-6+6=-2+6
x=4A line is perpendicular to the line given by the equation -8= 2y+3xWhat is theslope of the perpendicular line?
Answers
The slope of the perpendicular line is 2/3
Explanation:Give equation: -8 = 2y + 3x
Rewritting in the form of slope-intercept form: y = mx + c
2y + 3x = -8
2y = -3x - 8
divide both sides by 2:
2y/2 = -3x/2 - 8/2
y = -3x/2 - 4
y = -3/2 x - 4
Where m = slope = -3/2
c =intercept = -4
For a line to be perpendicualr to another line, the slope of one will be the negative reciprocal of the other one.
Slope of the 1st = -3/2
reciprocal of -3/2 = - 2/3
negative reciprocal = -(-2/3) = 2/3
The slope of the perpendicular line (slope of the second line) is 2/3
Answer:
slope of perpendicular line = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
- 8 = 2y + 3x ( subtract 3x from both sides )
- 8 - 3x = 2y ( divide through by 2 )
- 4 - [tex]\frac{3}{2}[/tex] x = y , that is
y = - [tex]\frac{3}{2}[/tex] x - 4 ← in slope- intercept form
with slope m = - [tex]\frac{3}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{3}{2} }[/tex] = [tex]\frac{2}{3}[/tex]
the length and width of a rectangle is in a ratio 3:2 find the area if the perimeter is 60 cm.
Answers
Given:
The ratio of the length and width of a rectangle is 3:2
The perimeter is 60 cm.
To find: Area of the rectangle
Explanation:
Let 3x and 2x be the length and breadth of the rectangle.
Using the formula of the perimeter,
[tex]\begin{gathered} P=2(l+b) \\ 60=2(3x+2x) \\ 60=2(5x) \\ 60=10x \\ x=6 \end{gathered}[/tex]So, the length and breadth are 18cm and 12cm.
The formula of area of the rectangle is,
[tex]\begin{gathered} A=l\times b \\ A=18\times12 \\ A=216cm^2 \end{gathered}[/tex]Final answer: The area of the rectangle is 216 square cm.
A train car is in the shape of a rign 4 41 feet 12 feet 09
Answers
Input data
w = 4.5 ft
l = 12
h = ?
V = 540 ft3
Procedure
[tex]\begin{gathered} V=w\cdot l\cdot h \\ h=\frac{V}{l\cdot w} \\ h=\frac{540}{4.5\cdot12} \\ h=10 \end{gathered}[/tex]
The answer would be h = 10 feet
2.6.PS-10Challenge Emily and Andy each go to a hardware store to buy wire. Thetable shows the cost y in dollars for x inches of the wire they need. Emilyneeds 25 feet of the wire. Andy needs 15 yards of the wire. How much willeach of them spend for wire?HELPPPP MEEEEE
Answers
First, we find the equation that represents the situation
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's replace the points (110,6.60) and (135,8.10) where,
[tex]\begin{gathered} x_1=110 \\ x_2=135 \\ y_1=6.60 \\ y_2=8.10 \end{gathered}[/tex][tex]m=\frac{8.10-6.60}{135-110}=\frac{1.5}{25}=0.06[/tex]Once we have the slope of the line, we use the point-slope formula to find the equation
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-6.60=0.06(x-110) \\ y=0.06x-6.6+6.6 \\ y=0.06x \end{gathered}[/tex]The equation that represents the problem is y = 0.06x.
Now, let's transform 25 feet and 15 yards into inches.
We know that 1 foot is equivalent to 12 inches, so
[tex]25ft\cdot\frac{12in}{1ft}=300in[/tex]We know that 1 yard is equivalent to 36 inches, so
[tex]15yd\cdot\frac{36in}{1yd}=540in[/tex]Then, we evaluate the equation for x = 300 and x = 540.
[tex]\begin{gathered} y=0.06x=0.06\cdot300=18 \\ y=0.06x=0.06\cdot540=32.4 \end{gathered}[/tex]Hence, Emily will spend $18 for 25 feet of wire, and Andy will spend $32.4 for 15 yards of wire.How far will the snowboarder travel in 14 seconds? Explain how you figured it out.
Answers
The snowboarder travels 105 meters in 7 seconds.
This means that the snowboarder travels 105/7 = 15 meters per second (m/s). So, his speed is 15 m/s
Therefore, in 14 seconds, the snowboarder will travel (15 meters per second)*(14 seconds) = 210 meters.
Suppose that a brand of lightbulb lasts on average 2710 hours with a standard deviation of 111hours. Assume the life of the lightbulb is normally distributed. Calculate the probability that aparticular bulb will last from 2426 to 2861 hours?P(2426 < X < 2861) =Enter your answer as a number accurate to 4 decimal places.*Note: all z-scores must be rounded to the nearest hundredth.
Answers
Answer:
P(2426 < X < 2861) =0.9079
Explanation:
• The average life of the bulb = 2710 hours
,• The standard deviation = 111 hours
We want to find the probability that a particular bulb will last from 2426 to 2861 hours.
Using the z-score formula below:
[tex]z=\frac{X-\mu}{\sigma}\text{ where }\begin{cases}{X=Raw\text{ Score}} \\ {\mu=Mean} \\ {\sigma=Standard\;Deviation}\end{cases}[/tex]We standardize each of the given values:
[tex]\begin{gathered} P\left(2426From the z-score table:[tex]P(-2.56The probability that a particular bulb will last from 2426 to 2861 hours is 0.9079.What is the exact value for the expression √52-√13+√117? Simplify if possible.4√13√132√398√39
Answers
Use the following property of the roots to find the answer if the problem.
[tex]\sqrt[]{a\cdot b}=\sqrt[]{a}\cdot\sqrt[]{b}[/tex][tex]\begin{gathered} \sqrt[]{52}-\sqrt[]{13}+\sqrt[]{117} \\ \sqrt[]{4\cdot13}-\sqrt[]{13}+\sqrt[]{9\cdot13} \\ \sqrt[]{4}\cdot\sqrt[]{13}-\sqrt[]{13}+\sqrt[]{9}\cdot\sqrt[]{13} \\ 2\sqrt[]{13}-\sqrt[]{13}+3\sqrt[]{13} \\ 4\sqrt[]{13} \end{gathered}[/tex]The right answer is the first option.
In Phoenix, Arizona, the average number of sunny days per year is 211. About what percent of the year is Phoenix sunny?
Answers
A year has 365 days, since 211 in average are sunny days this means that:
[tex]\frac{211}{365}\cdot100=58[/tex]percent of the year is sunny in Arizona.
A study is done on the number of bacteria cells in a petri dish. Suppose that the population size after hours is given by the following exponential function.
Answers
Given the exponential function:
[tex]P(t)=1800(1.03)^t[/tex]Where P models the population size after t hours. The initial population size can be obtained using t = 0:
[tex]\begin{gathered} P(0)=1800(1.03)^0=1800(1) \\ \therefore P(0)=1800 \end{gathered}[/tex]The initial population size is 1800.
Now, since the term inside the parentheses is greater than 1, we can conclude that this function represents a growth tendency.
Finally, we can take the ratio between the population size at time t and at time t+1:
[tex]\begin{gathered} \frac{P\left(t+1\right)}{P(t)}=\frac{1800(1.03)^{t+1}}{1800(1.03)t}=1.03=1+0.03 \\ \\ Change:\Delta=|1-\frac{P(t+1)}{P(t)}|=|1-1-0.03|=0.03 \end{gathered}[/tex]In percent form, the change is 3%
When you add two fractions that have the same denominator, you just need to add the4 3numerators and keep the denominator the same. For example,55 5. Rememberthat if you have an improper fraction (i.e., the top number is larger than the bottomnumber), then you need to change this to a mixed number by dividing the top by the1bottom. For example,Question 3Add ; and 2 and give your answer as a mixed fraction.
Answers
Since our fractions have the same denominator, we get
[tex]\frac{6}{4}+\frac{3}{4}\questeq\frac{6+3}{4}=\frac{9}{4}[/tex]and we must convert this result into a mixed fraction form. We can do this by taking the result of the division and the rest, that is,
then, the result is the final option.
Which describes the transtormation trom figure ABCDEF to figure A'B CD E F, andtells Whather the to fgures are similar or congruent?Ooilation, similar0 reflection, similarratatión, congruem2 translation, congruent
Answers
Answer: translation, congruent.
Explanation
• A dilation is an expansion o reduction of a figure.
,• A reflection is the image of a figure in a mirror.
,• A rotation is a circular movement around an axis or rotation.
,• A translation is moving a figure to a certain distance.
Based on this definitions, we can see that our figure A'B'C'D' describes a translation.
What is the reciprocal of -3.4?
Answers
The reciprocal of a number is the result obtained when 1 is divided by the number
Hence the reciprocal of -3.4 is
= 1/-3.4
= -1/3.4
= -0.2941
rinth grade DD. Area of parallelograms and trapezoids qsx What is the area? Write your answer as a fraction or as a whole or mixed number. square yards th
Answers
The parallel side of trapezoid is a = 1/4 and b = 3/4.
The height of trapezoid is h = 2/3.
The formula for the area of trapezoid is,
[tex]A=\frac{a+b}{2}\cdot h[/tex]Substitute the given value in the formula to obtain the area of trapezoid.
[tex]\begin{gathered} A=\frac{\frac{1}{4}+\frac{3}{4}}{2}\cdot\frac{2}{3} \\ =\frac{\frac{1+3}{4}}{2}\cdot\frac{2}{3} \\ =\frac{1}{2}\cdot\frac{2}{3} \\ =\frac{1}{3} \end{gathered}[/tex]So area of trapezoid is 1/3 square yards.
The trapezoid has a height of 16 m. Find the area.
Answers
The area of the trapezoid is 144 squared meters
Here, we want to find the area of the trapezoid
To find the area of the trapezoid, we need the measure of the top and bottom parallel side lengths
From the trapezoid midsegment theorem , the sum of the parallel sides is twice the length of the mid-segment
Since the midsegment is 9 m, then the sum of the considered parallel sides would be 2 * 9 = 18 m
Finally, we apply the formula for the area of the trapezoid as follows;
[tex]\begin{gathered} A\text{ = }\frac{1}{2}(a+b)h \\ h\text{ = height = 16 m} \\ (a+b)\text{ = sum of parallel side lengths = 18 m} \\ A\text{ =}\frac{1}{2}\times16\times18=144m^2 \end{gathered}[/tex](calculus !) The equation of the motion of a particle is s = 6t^2 + 5t + 2 where s is in meters and t is in seconds find the velocity as a function of t
Answers
The equation of motion is:
[tex]s=6t^2+5t+2[/tex]Recall that the velocity function v is given by:
[tex]v=\frac{ds}{dt}[/tex]Therefore,
[tex]v=12t+5[/tex]Therefore, the correct answer is choice B:
12t + 5
Find the value of h so the line that passes through (e,f) and (g,h) has a slope of 7. (Hint: Think about solving literal equations.)
Answers
Since the slope has to be 7:
[tex]\begin{gathered} \text{Let:} \\ (e,f)=(x1,y1)=(1,-2) \\ (g,h)=(x2,y2)=(3,12) \\ m=\frac{12-(-2)}{3-1}=\frac{14}{2}=7 \end{gathered}[/tex]about how many times greater is the distance from the sun to proxima centuries compared to the distance from sun to mercury? express your answer in scientific notation,using a whole number time a power of 101.4 x 10 x ^60.7 x 10 x ^66.9 x 10^56.9 x 10^7
Answers
Since we have that the distance from the Sun to Mercury is 3.6*10^7 and the distance from the sun to Proxima Centauri is 5.9*10^12, we proceed as follows:
[tex]f=\frac{5.9\cdot10^{12}}{3.6\cdot10^7}\Rightarrow f=\frac{1475000}{9}\Rightarrow f\approx163888.9[/tex]From this, we have that the distance from the Sun to Proxima Centauri is about 163889 times greater than that from the Sun to Mercury.
Three holes are dug for planting trees. The bottom of the holes, relative to the ground level, are -2 4/9, -2.475, and -2 11/15 what is the order farthest to closest
Answers
In the question we are told that the distance of the three holes relative to the ground level is
[tex]-2\frac{4}{9},-2.475\text{ and -2}\frac{11}{15}[/tex]Explanation
We can find the order of the farthest to the closest below:
The first step is to convert the set of given numbers into decimal points to get a better understanding of their values.
[tex]-2\frac{4}{9},-2.475\text{ and -2}\frac{11}{15}=-2.4444,2.475\text{ and -2.7333}[/tex]We can then arrange the values from the farthest to the closest. The number with the highest negative value represents the farthest, while the number with the smallest negative value represents the closest.
After re-arranging based on the above instruction, we have the answer as;
Answer:
[tex]-2.7333,-2.475,-2.4444[/tex]
f(x)=4x-5;g(x)=6x-3 find 3f(x)-2g(x)
Answers
f(x)=4x-5;g(x)=6x-3 find 3f(x)-2g(x)
we have that
3f(x)=3(4x-5)=12x-15
and
2g(x)=2(6x-3)=12x-6
so
3f(x)-2g(x)=(12x-15)-(12x-6)=-15+6=-9
answer is -9Jenny invests $3,072 in a savings accountwith a fixed annual interest ratecompounded continuously. After 8 years,the balance reaches $5,378.07. What isthe interest rate of the account?A) 6% B) 8%C) 79% D) 5%
Answers
Given:
Principal amount, P = $3,072
Time, t = 8 years
Final Amount, A = $5,378.07
To find the interest rate since it is compounded continuously, take the compound interest formula below:
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