Twice a number added to 6 is less than 23
[tex]2x+6<23[/tex]is 10 a possible solution. ?
In order to answer this question, we must solve for x
[tex]\begin{gathered} 2x+6<23 \\ 2x+6-6<23-6 \\ 2x<17 \\ \frac{2x}{2}<\frac{17}{2} \\ x<\frac{17}{2} \\ x<8.5 \end{gathered}[/tex]the solution is all numbers less than 8.5, therefore 10 is not a possible solution.
maya sells homemade spice mixes in different sizes at the creft fair. the graph shows the proportional relationship between tsp of cumin and tsp of chili powder in one recipe. what does the origin represent
The origin represents the quantities of chili powder and cumin are zero tsp in the recipe.
Maya sells homemade spice mixes in different sizes at the craft fair.
The given graph shows the proportional relationship between tsp of cumin and tsp of chili powder in one recipe.
As per the given graph,
The y-axis represents the tsp of chili powder in the recipe.
The x-axis represents the tsp of cumin in the recipe.
In the recipe, the proportions of chili powder and cumin are zero teaspoons which are represented by the origin of the given graph.
Therefore, the origin represents the quantities of chili powder and cumin are zero tsp in the recipe.
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slope of 1/3 and passing through the point (3,2)
To determine the equation of the line that has slope m=1/3 and passes through the point (3,2) you have to use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]Where
m is the slope of the line
(x₁,y₁) are the coordinates of one point of the line
Replace the formula above with the known information about the line:
[tex]y-2=\frac{1}{3}(x-3)[/tex]Next is to write the equation in slope-intercept form, which means that you have to leave the y term alone on the left side of the equation and all other terms have to be on the right side.
-First, distribute the multiplication on the parentheses term:
[tex]\begin{gathered} y-2=\frac{1}{3}\cdot3-\frac{1}{3}\cdot3 \\ y-2=\frac{1}{3}x-1 \end{gathered}[/tex]-Second, pass "-2" to the right side of the equation by applying the opposite operation, "+2", to both sides of the equal sign:
[tex]\begin{gathered} y-2+2=\frac{1}{3}x-1+2 \\ y=\frac{1}{3}x+1 \end{gathered}[/tex]So, the equation of the line with slope 1/3 that passes through the point (3,2), expressed in slope-intercept form is:
[tex]y=\frac{1}{3}x+1[/tex]Determine the center and radius of the following circle equation:2² + y² – 2x – 6y – 54 = 0Center:13Radius:Submit Answer
Answer:
Centre = (1, 3)
radius = 8units
Explanation:
The standard equaton of a circle is expressed as;
[tex]x^2+y^2+2gx+2fy+C\text{ = 0}[/tex]The radius of the circle is expressed as;
[tex]r=\sqrt[]{g^2+f^2-C^{}}[/tex]The centre is at C(-g, -f)
Given the expression;
[tex]x^2+y^2-2x-6y-54=0[/tex]Get the centre of the circle.
Compare both equations
[tex]\begin{gathered} 2gx=-2x \\ g\text{ = -1} \end{gathered}[/tex]similarly;
[tex]\begin{gathered} 2fy=-6y \\ 2f=-6 \\ f=-\frac{6}{2} \\ f=-3 \end{gathered}[/tex]The centre will be located at C(-(-1), -(-3)) = C(1, 3)
Next is to get the radius
Recall;
[tex]\begin{gathered} r=\sqrt[]{g^2+f^2-C} \\ r=\sqrt[]{(-1)^2+(-3)^2-(-54)} \\ r=\sqrt[]{1+9+54} \\ r=\sqrt[]{64} \\ r=8\text{units} \end{gathered}[/tex]Hence the radius is 8units
The number of students showing up for a high school football team is 10% smaller than the previous year. A few minutes before tryouts begin, another 5 students show up. There are 75 students on the field to try out for football. Which equation represents this situation?
Given data:
The expression for the given statement is,
[tex]0.9x+5=75[/tex]Thus, the option (C) is correct.
On your first day of work at the Vanity Fur Grooming Shop, you groomed 3 dogs between 7:45 a.m. and 2:30 p.m., taking breaks that totaled 45 minutes. Your supervisor advises that you will be scheduling your own appointments when customers call to have their pets groomed. If you continue to work at the same rate, how much time should you allow for each grooming appointment?
Answer:
2 hours
Explanation:
First, calculate the length of time between 7:45 a.m. and 2:30 p.m.
[tex]\begin{gathered} \; \; 2\colon30P.M\text{.} \\ -7\colon45A.M\text{.} \\ _{----------} \\ 6\colon45 \end{gathered}[/tex]If the break totaled 45 minutes, the time spent grooming the 3 dogs = 6 hours.
Therefore, if you continue to work at the same rate, the time that should be allocated for each grooming appointment:
[tex]\begin{gathered} =\frac{6}{3} \\ =2\text{ hours} \end{gathered}[/tex]Consider parallelogram ABCD below.Use the information given in the figure to find x, m ZADB, and m ZA.AB.3502x6m ZADB =m ZA = 11130С
ABCD is a parallelogram, which means that:
-The opposite sides are parallel, so AB || DC and AD || BC
-The opposite sides are congruent, so AB=DC and AD=BC
-Opposite angles are congruent
-Adjacent angles are supplementary
The congruent sides are equal which means that:
[tex]\begin{gathered} AD=BC \\ 2x=6 \end{gathered}[/tex]1) From this expression, you can determine the value of x, you have to divide both sides of the equal sign by 2:
[tex]\begin{gathered} \frac{2x}{2}=\frac{6}{2} \\ x=3 \end{gathered}[/tex]2) The opposite angles are equal, which means that ∠C=∠A=113º
3) Lines AD and BC are parallel lines intersected by a transversal line DB, so that:
∠CBD and ∠ADB are alternate angles, which means that they are congruent, so ∠CBD=∠ADB=35º
Angel is a senior in high school and works two jobs. He tutors for $20 per hour and walks dogs for $6 per hour. Angel's parents want him to work for no more than 18 hours per week. He wants to make at least $250 per week. Which system of linear inequalities represents this situation where t is the number of tutoring hours worked and w is the number of hours walking dogs E. t tw< 20 20t + 6w > 250 F. t tw 250 G. t +w< 250 20t + 6w< 18 H. 20t + 6w > 18 t + w > 18
Let:
t = time spent as tutor
w = time spent walking dogs
Angel's parents want him to work for no more than 18 hours per week, so:
t + w < 18
Besides, He tutors for $20 per hour and walks dogs for $6 per hour and He wants to make at least $250, so:
20t + 6w ≥ 250
Bob's Car Wash had to close 26 days last year because of bad weather. If last year had 365 days, what is the ratio of days closed to days open for Bob's Car Wash?OA. 26 to 339OB. 26 to 365OC. 365 to 26OD. 339 to 26
Days closed = 26
Days open = Total days - days closed = 365 -26 = 339
Days closed to days open:
26 to 339
In the diagram, line AB is parallel to DE. Also, line DE is drawn such that the length of line DE is half the length of line AB. If sin A=0.5, then what is sin E?
By alternate interior angle theorem. Angle A is congruent with Angle E.
This makes ΔAFB similar to ΔEFD.
IF sin A = 0.5, then sin E is also equal to 0.5.
Given the lengths of the three sides for ∆ABC, please list the angles in order from largest to smallest.
1. AB = 15, BC = 14, AC = 10
2. AC = 20, AB = 10, BC = 15
Answer:
1. ∠B, ∠A, ∠C2. ∠C, ∠A, ∠B
Step-by-step explanation:
We know smaller side is opposite to smaller angle and the larger side is opposite to larger angle.
Considering this we have the following1. AB = 15, BC = 14, AC = 10
Put in ascending order:
AC < BC < ABSo the opposite angles are:
B < A < C----------------------------------------------------------------------
2. AC = 20, AB = 10, BC = 15
Put in ascending order:
AB < BC < ACSo the opposite angles are:
C < A < BMatch each side length and angle to the correct answer. Simplify anyradicals.a= b=measure of angle C =measure of angle A=measure of angle B=c=
Given data:
The given figure of the triangle.
The measure of the side a is,
a=4 units.
The measure of the side b is,
b= 4 units.
The measure of the angle C is 90 degrees.
As the side a is equal to side b, it means the given triangle is isosceles right angle triangle.
The measure of the angle B is equal to the measure of the angle A which is 45 degrees.
The side c can be calculated as,
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=4^2+4^2 \\ c^2=32 \\ c=4\sqrt[]{2} \end{gathered}[/tex]Thus, a= 4 units, b=4 units, c=4√2, ∠C=90 degrees, ∠A= 45 degrees, and ∠B=45 degrees.
t - 3 > 2Solve the inequalities and represent the possible values of the variable on a number line.
Answer:
The solution to the inequality is;
[tex]t>5[/tex]drawing the variable on the number line;
Explanation:
Given the inequality;
[tex]t-3>2[/tex]To solve, let's add 3 to both sides of the inequality;
[tex]\begin{gathered} t-3+3>2+3 \\ t-0>5 \\ t>5 \end{gathered}[/tex]Therefore, the solution to the inequality is;
[tex]t>5[/tex]drawing the variable on the number line;
how do i determine if a(t)=-1.4t+96 is the plot on a graph?
EXPLANATION:
okay look at the question posed seems to be an equation of an acceleration graph where acceleration is equal to speed over time, but the graph given by the exercise is needed to determine exactly what variables it is, but to find the possible values of a you must give t values to graph t on the x-axis and a on the y-axis.
Sasha owes a total of $1,845.00 on revolving credit accounts that have total limits of $4,500.00. Calculate the amount she needs to pay on her debt to reduce her revolving credit accounts to reach a 25% debt-to-credit ratio. $705.00$720.00$988.00$1,125.00
Sashas total debt is 1845
Total limit on the credit card account is 4500
25 × 4500 / 100 = 1125
25% of 4500 is 1125
So in order to reach a 25% debt to credit ratio Sasha needs to payback 720 of her debt.
1845 - 1125 = 720
Option B is the answer
☆
13. The amount of ice cream in an ice cream cone has a distribution with a mean amount of 3.2 ounces
per cone and a standard deviation of 0.6 ounces. If there are 40 kids at a birthday party, what is
the probability that more than 138 ounces of ice cream will be served? (Hint: Find average amount
of ice cream served per kid at the party)
The probability that more than 138 ounces of ice cream will be served is; 0.33845 or 33.845%
How to find the probability from the z-score?
The formula for calculation of the test statistic or z-score of a population in normal distribution is given as;
z = (x' - μ)/σ
where;
z is z-score
x' is sample mean
μ is population mean
σ is standard deviation
We are given;
Population mean; μ = 3.2
Standard deviation; σ = 0.6
We don't have sample means but we are told that there are 40 kids and we want to find the probability that more than 138 ounces of ice cream will be served. Thus;
Sample mean; x' = 138/40 = 3.45
Thus;
z = (3.45 - 3.2)/0.6
z = 0.417
From online p-value from z-score calculator, we have;
probability = 0.33845 = 33.845%
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what is 1+1how old are you
1 + 1 in base 10 is 2
A( graph the system (Let t be represented by the hot axis and p be represented by the vertical axis B) find the solution to the system (t p)
I) p = 3.5t + 5
II) p = 7t/2 - 5
A) For equation I, if we replace t with 0 we find p = 5 and if we replace t with 2 we find p = 3.5*2 + 5 = 12. Therefore, to graph the line represented by this equation, we just need to draw a line passing through the points (0,5) and (2,12)
For equation II, if we replace t with 0 we find p = -5 and if we replace t with 2 we find p = (7/2)*2 - 5 = 2. Therefore, to graph the line represented by this equation, we just need to draw a line passing through the points (0,-5) and (2,2).
Here is the system represented by a graph:
B) By the graph, we can see that the lines are parallel and never intercept each other. This happens because they have the same slope (3.5 = 7/2). Therefore, this system has no solution.
Suppose your final grade in this class is based on the following system:Class participation 10% homework 20%test average 30% final exam 25%quiz average 15%Given the grades listed below, what would your final grade in the class be?test grades(78, 87, 93, 75) quiz average (85)Class participation (95) homework(75)final exam(63)choices:A. 83B. 70C. 88D. 78
to find a percentage we multiply by the number and divide by 100
class participation
[tex]\begin{gathered} 95\times\frac{10}{100} \\ =9.5 \end{gathered}[/tex]homework
[tex]\begin{gathered} 75\times\frac{20}{100} \\ =15 \end{gathered}[/tex]test average
first find the average
[tex]\begin{gathered} \frac{78+87+93+75}{4} \\ =83.25 \end{gathered}[/tex]then the percentage
[tex]\begin{gathered} 83.25\times\frac{30}{100} \\ =24.975 \end{gathered}[/tex]Final Exam
[tex]\begin{gathered} 63\times\frac{25}{100} \\ =15.75 \end{gathered}[/tex]Quiz average
[tex]\begin{gathered} 85\times\frac{15}{100} \\ =12.75 \end{gathered}[/tex]finally we add to get the final grade
[tex]\begin{gathered} 9.5+15+24.975+15.75+12.75 \\ =77.97 \end{gathered}[/tex]the final grade is 78
(a) Which function has the graph with a y-intercept closest to 0 ?(b) Which function has the graph with the greatest slope?(c) Which functions have graphs with y-intercepts greater than 3? (Check all that apply.)
We need to find the slope-intercept equation for all cases:
Function 1.
In this case, we have the following points
[tex]\begin{gathered} (x_1,y_1)=(1,-2) \\ (x_2,y_2)=(0,-4) \end{gathered}[/tex]Then, its slope is given by
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-4+2}{0-1}=2[/tex]Since the line crosses the y-axis at y=-4, the line equation is:
[tex]y=2x-4[/tex]Function 2.
We can choose 2 points of the table, for instance,
[tex]\begin{gathered} (x_1,y_1)=(0,5) \\ (x_2,y_2)=(1,4) \end{gathered}[/tex]and get the following slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-5}{1-0}=-1[/tex]since the line crosses at y=5, the equation is:
[tex]y=-x+5[/tex]Function 3.
From the given information, the equation is
[tex]y=-4x-1[/tex]Function 4.
From the given information, the equation is:
[tex]y=5x+2[/tex]In summary, we have obtained the following equations:
1) y=2x-4
2) y=-x+5
3) y=-4x-1
4) y=5x+2
Then, we have obtained:
a) Which function has the graph with a y-intercept closest to 0? Answer. As we can note, function 3 because its y-intercept is -1
(b) Which function has the graph with the greatest slope? Answer. From the above result, we can note that function 4 has the greatest slope because it is equal to 5
(c) Which functions have graphs with y-intercepts greater than 3? Answer. Only function 2 has y-intercept greater than 3 because the value is 5
In summary, the answers are:
a) Function 3
b) Function 4
c) Function 2
Given f(x)=1/x-2 and g(x)=square root of x+2, what is the domain of f (g(x))?.A. ℝB. [–2, ∞)C. [–2, 2) ∪ (2, ∞)D. (–∞, 2) ∪ (2, ∞)
we have the functions
[tex]\begin{gathered} f(x)=\frac{1}{x-2} \\ \\ g(x)=\sqrt{x+2} \end{gathered}[/tex]Find out f(g(x))
[tex]f\mleft(g\mleft(x\mright)\mright)=\frac{1}{\sqrt{x+2}-2}[/tex]Remember that
The radicand must be greater than or equal to zero and the denominator cannot be equal to zero
so
step 1
Solve the inequality
[tex]\begin{gathered} x+2\ge0 \\ x\operatorname{\ge}-2 \end{gathered}[/tex]the solution to the first inequality is the interval [-2, infinite)
step 2
Solve the equation
[tex]\begin{gathered} \sqrt{x+2}-2\ne0 \\ \sqrt{x+2}\operatorname{\ne}2 \\ therefore \\ x\operatorname{\ne}2 \end{gathered}[/tex]The domain is the interval
[–2, 2) ∪ (2, ∞)
The answer is the option CIt’s multi-step linear equations I have to solve for the x but in this question is asking “expand, and then solve for x” what did it mean by expand 5a - (2a + 15) = 24
Given:
[tex]5a-(2a+15)=24[/tex]To expand and solve for x:
On expanding the given expression, we have,
[tex]5a-2a-15=24[/tex]On solving we get,
[tex]\begin{gathered} 3a-15=24 \\ 3a=24+15 \\ 3a=39 \\ a=13 \end{gathered}[/tex]Therefore, the value of a is 13.
What is the measure of the missing side of the right triangle? Sad see is the hypotenuse. Sides a and b are the legs
Using the Pythagorean theorem, the formula is:
[tex]a^2+b^2=c^2[/tex]Where:
a = 7.1 km
c = 8.4 km
And we will find the side b.
Substitute the values:
[tex]7.1^2+b^2=8.4^2[/tex]And solve for b:
[tex]\begin{gathered} 50.41+b^2=70.56 \\ \text{subtract 50.41 on both sides} \\ 50.41+b^2-50.41=70.56-50.41 \\ b^2=20.15 \\ b=\sqrt[]{20.15}=4.5 \end{gathered}[/tex]Answer: b = 4.5 km
Which equation shows the relationship between the variables in the table? number of packs of markers(m) 012345 cost in dollars (d) 048121620
The equation shows the relationship between the variables is y = 10.53x.
To show the relationship between the variables in the table:
Given m = 012345, d = 048121620
m d k
0 0 0
1 4 4
2 8 4
3 1 0.33
4 2 2
5 1 0.2
Total = 10.53
This constant represents the ratio between the two variables. This ratio will be the same for every set of ordered pairs that represent the relationship.
Equation: A proportional relationship can be represented by the equation y = kx y = k x , where k is the constant ratio.
Therefore, by substituting the value of k in the above equation, we get:
y = 10.53x
Hence the answer is the equation shows the relationship between the variables is y = 10.53x.
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Solve using the quadratic formula. x^2 +27=0 Enter your answers, as exact values, in the boxes x= or x=
By using the quadratic formula, the values of x are:
x = + 3√3ix = - 3√3iWhat is the quadratic formula?The quadratic formula is used to find the roots of a quadratic equation and these roots are called the solutions of the quadratic equation. A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients.However, there are several methods of solving quadratic equations such as factoring, completing the square, graphing, etc.So, the equation is: x² + 27 = 0
The quadratic formula: -b±√b²-4ac/2aNow, use the quadratic formula as follows:
x = 0 ± √0 - 4(27)/2ax = ± √-108/2x = 2(±√-27/2)x = ±√-27x = ±3√3iTherefore, by using the quadratic formula, the values of x are:
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Can you please help me out with a question
Explanation
we have a rigth triangle, then
Let
leg1=radius= 7
leg2=QP
hypotenuse= radius+18=25
now, we can use the Pythagorean theorem:
Pythagorean theorem, the geometric theorem that states the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse
[tex]a^2+b^2=c^2[/tex]hence, replace
[tex]\begin{gathered} 7^2+QP^2=25^2 \\ 49+QP^2=625 \\ \text{subtract 49 in both sides} \\ 49+QP^2-49=625-49 \\ QP^2=576 \\ \text{square rot in both sides} \\ \sqrt[\square]{QP^2}=\sqrt[\square]{576} \\ QP=24 \end{gathered}[/tex]so, the answer is
[tex]J.24[/tex]I hope this helps you
How can i solve this?
Answer:
3791m
Explaation:
We are given the following from the diagram;
Ocean surface = adjacent side = x
hypotenuse = 3900m
Angle of depression = 76.4 degrees
According to SOH
sin theta = opp/hyp
sin 76.4 = opp/3900
Opp = 3900sin76.4
Opp = 3900*0.9719
Opp = 3,790.41
The distance below the ocean surface is approximately 3791m
Tim bought a pair of Zeus running shoes on sale that were marked down 20% to $100 what was the original price of the shoes
Given:
Tim bought a pair of shoes for $100 on 20% down.
Let 'x' be the original price of the shoes.
Percentage of amount paid for the shoes is 80%
[tex]100=x\times\frac{80}{100}[/tex][tex]100\times\frac{100}{80}=x[/tex][tex]x=\frac{10000}{80}[/tex][tex]x=125[/tex]Therefore, the original price of the shoes is $125
4 Find the slope of the line that passes through the points (- 4.6) and (-4,-2)
to finde the slope of the poins we use the formula
[tex]m=\frac{y2-y1}{x2-x1}[/tex]after replacing on the formula we obtain
[tex]\begin{gathered} m=\frac{-2-6}{-4-4} \\ m=\frac{-8}{-8} \\ m=1 \end{gathered}[/tex]the slope for the line will be 1
Inverse VariationThe variable y is inversely proportional to x if there is a nonzero constant, k, such that y=k/x.The number k is called the constant of variation or the constant of proportionality.Now, suppose that y is inversely proportional to x. If y is 2 when x is 7, we can find the constant of proportionality by first solving for k and then rewriting the equation to create an inverse variation equation.Start by substituting the values for y and x in to the standard equation and solve for k:2=k/714=ky=14/xPart AUse the equation we just found to determine the value of y when x = 21. Part BFind the value of x when y = 28. Part CLet’s look at a real-world example using inverse variation.In physics, Boyle’s law states that if the temperature is constant, then the pressure, P, of a gas is inversely proportional to the volume, V, of the gas. If the pressure of the gas in a cylinder is equal to 250 kilopascals when the volume of the container is 1.7 cubic meters, then determine the constant of proportionality for this situation. Show your work. Part DUse the constant of proportionality from part C to write an inverse variation equation to model this situation. Part EUsing the equation from part D, determine what the pressure would be in the container if the size of the container were to increase to 3.2 cubic meters. Part FWhat would the approximate volume need to be if you wanted the pressure to be 150 kilopascals? Part GReturning to the situation from part C, assume that the container was stored in a cooler room. Now, as the temperature of a gas increases, the pressure of the gas increases. Similarly, if the temperature of the gas decreases, the pressure of the gas decreases.So, assuming the container was placed in a cooler room, you know that the temperature of the gas has decreased by an unknown amount. Write an inequality to model this new situation. Part HUse the inequality from part G to write an inequality that represents the possible pressure of the gas if it is placed in a 3 cubic meter container. Give your answer in the form P < #. Part IYour answer from part H includes an infinite number of possibilities. However, in terms of this situation, some of the possible values are extraneous solutions. These are solutions that do not work given the situation. Rewrite your answer to remove any extraneous solutions and explain your answer.
Part A)
According to the text, the equation that relates x and y is:
[tex]y=\frac{14}{x}[/tex]Substitute x=21 to find the value of y when x=21:
[tex]y=\frac{14}{21}[/tex]Simplify the expression:
[tex]\frac{14}{21}=\frac{7\cdot2}{7\cdot3}=\frac{2}{3}[/tex]Therefore, the value of y when x=21 is:
[tex]\frac{2}{3}[/tex]Part B)
To find the value of x when y=28, substitute y=28 and solve for x:
[tex]\begin{gathered} y=\frac{14}{x} \\ \Rightarrow28=\frac{14}{x} \\ \Rightarrow28x=14 \\ \Rightarrow x=\frac{14}{28} \\ \therefore x=\frac{1}{2} \end{gathered}[/tex]Therefore, the value of x when y=28 is:
[tex]\frac{1}{2}[/tex]Part C)
Since the pressure P is inversely proportional to the volume V, then:
[tex]P=\frac{k}{V}[/tex]Solve for k and substitute P=250kPa and V=1.7m^2 to find the constant of proportionality:
[tex]\begin{gathered} \Rightarrow k=PV \\ =(250\text{kPa})(1.7m^3) \\ =425\text{kPa}\cdot m^3 \end{gathered}[/tex]Therefore, the constant of proportionality for this situation is:
[tex]425\text{ kPa}\cdot m^3[/tex]Part D)
Substitute the value of k into the equation that shows the inverse relation between P and V:
[tex]\begin{gathered} P=\frac{k}{V} \\ \Rightarrow P=\frac{425\text{ kPa}\cdot m^3}{V} \end{gathered}[/tex]Therefore, the inverse variation equation model for this situation, is:
[tex]P=\frac{425\text{ kPa}\cdot m^3}{V}[/tex]Part E)
Substitute V=3.2m^3 to find the pressure under those conditions:
[tex]\begin{gathered} P=\frac{425\text{ kPa}\cdot m^3}{3.2m^3} \\ =132.8\text{kPa} \end{gathered}[/tex]Therefore, the pressure would be:
[tex]132.8\text{kPa}[/tex]Part F)
Isolate V from the equation and substitute P=150kPa:
[tex]\begin{gathered} V=\frac{425\text{ kPa}\cdot m^3}{P} \\ =\frac{425\text{ kPa}\cdot m^3}{150\text{ kPa}} \\ =2.83m^3 \end{gathered}[/tex]Therefore, the approximate volume would have to be equal to:
[tex]2.83m^3[/tex]Part G)
Since the temperature has decreased, the pressure must be lower according to the description provided in the text. Then, an inequality to model this situation would be:
[tex]P<\frac{k}{V}[/tex]Part H)
Substitute the value of k and V=3m^3:
[tex]\begin{gathered} P<\frac{425\text{ kPa}\cdot m^3}{3m^3} \\ \Rightarrow P<141.7\text{ kPa}^{} \end{gathered}[/tex]Part I)
Mathematically, all numbers under 141.7 satisfy the inequality from part H. Nevertheless, negative pressures do not have a physical meaning under the context of the Ideal Gas Law. Therefore, we must include the condition that P is greater than 0:
[tex]0b -6(46 - 2) = 150A) 4-6 B) -5C) 9 D) (3)
To solve this equation, we need to follow the next steps:
1. Apply the distributive property:
[tex]b-6\cdot4b+6\cdot2=150\Rightarrow b-24b+12=150[/tex]2. Add the like terms, and subtract 12 to both sides of the equation:
[tex]-23b+12=150\Rightarrow-23b=150-12[/tex]3. Divide both sides of the equation by -23 (to isolate b):
[tex]\frac{-23}{-23}b=\frac{150-12}{-23}\Rightarrow b=\frac{138}{-23}\Rightarrow b=-6[/tex]Then, the answer to this equation is {-6} (option A).