we get that the equation that models this situation is:
[tex]L=9m+124[/tex]where L is the number of liters and m the minutes. So we have that
[tex]151=124+9m\rightarrow m=\frac{151-124}{9}=3[/tex]so after 3 minutes the tank jas 151 liters
[tex]191.5=124+9m\rightarrow m=\frac{191.5-124}{9}=7.5[/tex]so after 7.5m the tanks has 191.5 liters
and for the last one we get
[tex]x=9y+124\rightarrow y=\frac{x-124}{9}[/tex]Fill in the blank __(x+6)+8(x+6) =4x+24
We want to fill in the blank in the equation;
let's represent the blank with a.
[tex]_{}a(x+6)+8(x+6)=4x+24[/tex]Let's factorize the right side of the equation.
[tex]\begin{gathered} a(x+6)+8(x+6)=4x+24 \\ a(x+6)+8(x+6)=4(x+6) \end{gathered}[/tex]and also the left side;
[tex]\begin{gathered} a(x+6)+8(x+6)=4(x+6) \\ (a+8)(x+6)=4(x+6) \end{gathered}[/tex]Then let's divide both sides by (x+6);
[tex]\begin{gathered} (a+8)(x+6)=4(x+6) \\ \frac{(a+8)(x+6)}{(x+6)}=\frac{4(x+6)}{(x+6)} \\ (a+8)=4 \end{gathered}[/tex]Then we can solve for a in the resulting equation.
subtract 8 from both sides.
[tex]\begin{gathered} a+8=4 \\ a+8-8=4-8 \\ a=-4 \end{gathered}[/tex]Therefore, the value to fill into the blank is -4
[tex]-4(x+6)+8(x+6)=4x+24[/tex]what is the distance from the origin to point P graphed on the complex plane below?√7√29729
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
From the graph, we can see that:
Using the Pythagoras' theorem,
[tex]\begin{gathered} p^2=2^{2\text{ }}+5^2 \\ p^2=\text{ 4+ 25} \\ p^2=\text{ 29} \\ \text{square}-\text{root both sides, we have that:} \\ p\text{ =}\sqrt[]{29} \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]\sqrt[]{29}[/tex]Find the equation of a line perpendicular to y = - 1/4 x + 9 that passes through the point (4, - 8) .
perpendicularWe were given the following information:
The equation of a line is given by: y = - 1/4 x + 9
We want to obtain the equation for a line perpendicular to this line & that passes through the point (4, -8). This is shown below:
The general equation of a straight line is given by:
[tex]\begin{gathered} y=mx+b \\ where\colon \\ m=slope \\ b=y-intercept \end{gathered}[/tex]The equation of the line given us is:
[tex]\begin{gathered} y=-\frac{1}{4}x+9 \\ \text{Comparing this with the general equation, we will deduce that:} \\ mx=-\frac{1}{4}x \\ m=-\frac{1}{4} \\ \text{Thus, the slope of this line is: }-\frac{1}{4} \end{gathered}[/tex]The relationship between the slope of a line and the slope of a line perpendicular to it is given by the statement "the product of the slopes of two lines perpendicular to one another is negative one"
This is expressed below:
[tex]\begin{gathered} m\times m_{perpendicular}=-1 \\ m_{perpendicular}=-\frac{1}{m} \\ m=-\frac{1}{4} \\ m_{perpendicular}=\frac{-1}{-(\frac{1}{4})} \\ m_{perpendicular}=4 \\ \\ \therefore m_{perpendicular}=4 \end{gathered}[/tex]Therefore, the slope of the perpendicular line is: 4
We were told that the perpendicular line passes through the point (4, -8). We will obtain the equation of the perpendicular line using the Point-Slope equation. This is shown below:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ (x_1,y_1)=(4,-8) \\ m\Rightarrow m_{perpendicular}=4_{} \\ \text{Substitute the values of the variables into the initial equation above, we have:} \\ y-\mleft(-8\mright)=4(x-4) \\ y+8=4(x-4) \\ y+8=4x-16 \\ \text{Subtract ''8'' from both sides, we have:} \\ y=4x-16-8 \\ y=4x-24 \\ \\ \therefore y=4x-24 \end{gathered}[/tex]The graphical representation of this is given below:
I need help checking my answers to simplifying expressions. -2n-(9-10n)
We are given the following expression
[tex]-2n-(9-10n)[/tex]We are asked to simplify the above expression.
First of all, expand the parenthesis.
[tex]\Rightarrow-2n-9+10n[/tex]Now, combine the like terms together and simplify
[tex]\begin{gathered} \Rightarrow10n-2n-9 \\ \Rightarrow8n-9 \end{gathered}[/tex]Therefore, the simplified expression is
[tex]8n-9[/tex]how to solve 5x+5=2x+20
To do this you can subtract 5 from both sides of the equation
[tex]\begin{gathered} 5x+5=2x+20 \\ 5x+5-5=2x+20-5 \\ 5x=2x+15 \end{gathered}[/tex]Now you can subtract 2x from both sides of the equation
[tex]\begin{gathered} 5x=2x+15 \\ 5x-2x=2x+15-2x \\ 3x=15 \end{gathered}[/tex]Finally, you can divide by 3 both sides of the equation
[tex]\begin{gathered} \frac{3x}{3}=\frac{15}{3} \\ x=5 \end{gathered}[/tex]On the other hand, to check you replace the value of x found in the original expression
[tex]\begin{gathered} 5x+5=2x+20 \\ 5(5)+5=2(5)+20 \\ 25+5=10+20 \\ 30=30 \end{gathered}[/tex]Since a true equality is obtained, then it is true that the value of x is 5.
I need help with a question for my math practice but I will have to see the picture to show you
The dependent variable is Y because the value depends on the number of people(x) who buy tickets
and y is the total cost of the tickets
Then the right option is D
In the United States, 1000 residents aged 15 or older were surveyed and 870 replied that they were satisfied with the water quality. The 90% confidence interval estimate of all U.S residents satisfied with their water quality is _________.
Given:
Here In the United States, 1000 residents aged 15 or older were surveyed and 870 replied that they were satisfied with the water quality is given.
Required:
Interval of 90% confidence level.
Explanation:
The formula to find the interval of confidence level is as below
[tex]=(p^{\prime}-z*\sqrt[]{\frac{p^{\prime}(1-p^{\prime})}{n}},\text{p' }+z*\sqrt[]{\frac{p^{\prime}(1-p^{\prime})}{n}})[/tex]Now we have to find the value of all
z=1.64485
p'=870/1000=0.87
n=1000
Now put the all values
[tex](0.87-1.64485*\sqrt[]{\frac{0.87(1-0.87)}{1000}},0.87+1.64485*\sqrt[]{\frac{0.87(1-0.87)}{1000}})[/tex][tex](0.87-0.0175,0.87+0.0175)[/tex][tex](0.8525,0.8875)[/tex]Final answer:
Confidence interval is (0.8525,0.8875)
You are playing a dice game and wondering whatnumber has been rolled the most so far.Find the mode of the following rolls:2, 1, 5, 6, 6, 3, 1, 4, 4, 3, 2, 1, 5, 1, 5, 3
Solution:
Concept:
Definition of mode:
Mode: The most frequent number—that is, the number that occurs the highest number of times.
The numbers are given below as
[tex]2,1,5,6,6,3,1,4,4,3,2,1,5,1,5,3[/tex]By rearranging the numbers, we will have
[tex]1,1,1,1,2,2,3,3,3,4,4,5,5,5,6,6,[/tex]From the set of numbers above, we will see that the number that occurs most is 1
Hence,
The mode of the rolls is
[tex]\Rightarrow1[/tex]A 12 ounce can of beans costs $0.88. What is the unit price per ounce?
To find the unit price per ounce of beans, you just need to divide the cost of the 12 ounce can by the number of ounces of beans in the can, it means, 12.
[tex]\frac{0.88}{12}=0.0733[/tex]The unit price per ounce is $0.0733, that rounded to the nearest hundredth is $0.07.
Consider ADEF with vertices D(-6,4) E(0,8), and F(2,-2) Find the coordinates of the vertices of the final image of ADEF after the similarity transformation Translation: (x,y) - (x + 8y + 4) Dilation: (x,y)-(1/2x, 1/2y) centered at (0,0) The coordinates of the vertices of the final image are D'' E" and F"
D''(1, 4), E"(4, 6) and F"(5, 1)
Explanation:Coordinates of original image: D(-6,4), E(0,8) and F(2,-2)
Translation: (x,y) to (x + 8, y + 4)
The coordinate becomes:
D(-6,4) = (-6+8, 4+4) = (2, 8)
E(0,8) = (0+8, 8+4) = (8, 12)
F(2,-2) = (2+8, -2+4) = (10, 2)
Dilation: (x,y) to (1/2x, 1/2y) centered at (0,0)
D" = (2, 8) to 1/2(2), 1/2(8) = (1, 4)
E" = (8, 12) to 1/2(8), 1/2(12) = (4, 6)
F" = (10, 2) to 1/2(10), 1/2(2) = (5, 1)
The coordinates of the vertices of the final image are D''(1, 4), E"(4, 6) and F"(5, 1)
Sara runs along a circular track. The diameter of the track is 75 yards. She will jog 2 laps around the track. Which is the closest to the amount of yards Sara will run?
Sara will run 8836 square yards
Explanation:Given that the diameter of the track Sara runs is 75 yards.
The radius is half the diameter, and so, 37.5
Sara will jog 2 laps around the track, therefore, the amount of yards Sara will run is obtained by finding twice the area of the circle she is going to cover.
Area of a circle is:
[tex]A=\pi r^2[/tex]Where r is the radius
Using r = 37.5
[tex]\begin{gathered} A=\pi(37.5)^2 \\ =1406.25\pi \\ =4417.9 \end{gathered}[/tex]Since she is jogging 2 laps, we have the yards she will cover to be:
2(4417.9)
= 8835.8
Approximately 8836 square yards
Question 10The physical plant at the main campus of a large state university recieves daily requests to replace florecentlightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 56 and a standarddeviation of 11. Using the Empirical Rule rule, what is the approximate percentage of lightbulb replacementrequests numbering between 56 and 89?Do not enter the percent symbol.ans =%
We know that the empirical rule states that 99.7% of the area is in the interval:
[tex](\mu-3\sigma,\mu+3\sigma)[/tex]In this case we notice that we are looking at the interval (56,89) in a normal distribution with mean 56 and standard deviation 11, which means that we area in the interval:
[tex](\mu,\mu+3\sigma)[/tex]which means that we have half the area of the interval mentioned before. Therefore, the approximate percentage between 56 and 89 is 49.85%
twice a number increased by 7 is 35 . find the number
Hello there. To solve this question, we'll have to remember how to translate a statement to a mathematical equation and then solve the equation for a number.
Twice a number increased by 7 is 35. We want to find that number.
In this case, say this number is n.
Twice this number is the same as multiplying this number by 2, hence
[tex]2n[/tex]Now increasing it by 7 is the same as adding 7 to the expression, therefore
[tex]2n+7[/tex]And this must be equal to 35
[tex]2n+7=35[/tex]Now we have to solve this equation for n.
Subtract 7 on both sides of the equation
[tex]2n=28[/tex]Divide both sides of the equation by a factor of 2
[tex]n=14[/tex]This is the number we're looking for.
Mary has been getting up extra early on school days so far she has woken up 6 out of 80 school days what percent of the days has she get been getting up early
Let's begin by identifying key information given to us:
Number of times she woke early (e) = 6
Total number of days (t) = 80 days
The percentage of days she's been getting up early is given by:
[tex]\begin{gathered} \text{\%}n\text{=}\frac{e}{t}\cdot100\text{\%} \\ \text{\%}n=\frac{6}{80}\cdot100\text{\%} \\ \text{\%}n=7.5\text{\%} \end{gathered}[/tex]Mary has gotten up early 7.5% of the days
What is the greatest common factor of 63, 84, and 105?
Answer:
Explanation:
The factors of 63 are: 1, 3, 7, 9, 21, 63
The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 1
What is the process between the second and third step? I don’t get how step 3 has 10^2 power.
ANSWER
Base raised to logarithm rule
EXPLANATION
Between the second and third steps, a property of logarithms was applied, the base raised to logarithm rule. This property states that when the base of the logarithm is raised to the logarithmic expression, the result is the argument,
[tex]a^{\log_a(x)}=x[/tex]In this case, we can see that it only says "log", so we can assume that the base of this logarithm is 10. To get from step 2 to step 3, we have to raise the base (10) to each side of the equation,
[tex]10^{\log(\frac{x+2}{x+1})}=10^2[/tex]And then, by the property stated above, we have the third line of this solution,
[tex]\frac{x+2}{x+1}=10^2[/tex]In the picture, the equation is inverted, but since there is an equal sign it is equivalent.
Hi!! I have a homework problem i am not sure how to do.. I have missed some school due to health related issues so i’m a little behind. Thank you so much. I also have an example of the answer i have to give i can send to you
We need to find a quadratic model from the news or social media.
We can model the number of people watching a story after t time of posting it.
When you post it, there are no people watching it, it starts at y=0. Throughout the day more people are watching, but when time passes, the number of people starts to decrease.
The situation can be modeled by the quadratic function:
[tex]y=-0.5x^2+10x[/tex]Where x is the time in hours after posting the story, and y is the number of new people who watched the story in the past hour.
If we graph the function it looks like this:
As can be seen, at the beginning the number of people watching the story starts to increase, but after some time the number of people you reach out to with your story starts to decrease until no one will watch it.
The quadratic term of the function is:
[tex]-0.5x^2[/tex]The coefficient of the quadratic term determines how wide or narrow the graphs are, and whether the graph turns upward or downward. As we have a negative coefficient, then the parabola opens down.
The linear term is 10x, and it determines the position of the vertex.
There is a maximum value and it occurs at t=10 when you reach out to 50 people: (10,50).
The domain of the function is the set of possible x-values, as can be seen in the graph, it is [0,20], which means after 20 hours no one will watch your story.
The range is the set of y-values the function takes. It is [0,50]. It means you start with 0 people and the maximum number of people you reach out to in one hour is 50.
Please help meif you can't read it it says -138=-6(6b-7)
We have the following:
[tex]\begin{gathered} -138\ge-6\cdot(6b-7) \\ \end{gathered}[/tex]solving for b:
[tex]\begin{gathered} -6\cdot(6b-7)\le-138 \\ -\frac{6}{6}\cdot(6b-7)\le-\frac{138}{6} \\ -(6b-7)\le-23 \\ (6b-7)\ge23 \\ 6b-7+7\ge23+7 \\ 6b\ge30 \\ b\ge\frac{30}{6} \\ b\ge5 \end{gathered}[/tex]Therefore, the interval is:
[tex]\lbrack5,\infty)[/tex]Which of the graphs is represented by the following table:X-2 -1 0 1 2y1 2 3 4 5Click the button BELOW the correct graph.2+23442++22++2-3+432++2Show
Let us prepare the table from the deduced information as shown below:
We can use a graphing calculator to plot the points.
The graph is shown below:
4Which expression is equivalent to 3*25?--45+34 1 1+3x+4³03x-y-4 5+3+3X-3x - 1 - 1 - 3 x -1 13X-43 152+3544YyIN1|2
Explanation
If we look at the given options we can see that
[tex]\begin{gathered} \frac{1}{3}x-\frac{1}{4}y-\frac{4}{5}+\frac{1}{3}x-\frac{1}{4}y \\ rearrange\text{ terms} \\ =\frac{1}{3}x+\frac{1}{3}x-\frac{1}{4}y-\frac{1}{4}y-\frac{4}{5} \\ =\frac{x+x}{3}-\frac{y+y}{4}-\frac{4}{5} \\ =\frac{2x}{3}-\frac{2y}{4}-\frac{4}{5} \\ =\frac{2x}{3}-\frac{1}{2}y-\frac{4}{5} \end{gathered}[/tex]Answer: Option 2
the volume of the cone.Radius: 5 m, Height: 5 mnd to the nearest whole number.Volume[ ? ] m³
EXPLANATION
The volume of the cone is given as;
[tex]V=\frac{1}{3}\pi r^2h=\frac{1}{3}\pi\times5^2\times5=\frac{125}{3}\pi\approx131m^3[/tex]Answer: 131 cubic meteres
if measure of arc JI= (3x+2), measure of arc HLK= (15x+36), and measure of angle HMK=(8x-1), find the measure of arc HLK.
Step 1: Problem
If the measure of arc JI= (3x+2), a measure of arc HLK= (15x+36), and a measure of angle HMK=(8x-1), find the measure of arc HLK.
Step 2: Concept
Apply secant theorem
[tex]\text{HMK = }\frac{1}{2}(\text{ }JI\text{ + HLK )}[/tex]Step 3: Method
Given data
[tex]\begin{gathered} 8x\text{ - 1 = }\frac{1}{2}\text{ ( 3x + 2 + 15x - 36 )} \\ (8x\text{ - 1 ) }\times\text{ 2 = 18x - 34} \\ 16x\text{ - 2 = 18x - 34} \\ 34\text{ - 2 = 18x - 16x } \\ 32\text{ = 2x} \\ x\text{ = 32/2} \\ x\text{ = 16} \end{gathered}[/tex]The measure of arc HLK = 15x - 36
= 15(16) - 36
= 240 - 36
= 204
Step 4: Final answer
arc HLK = 204
ActivityPlane A is descending toward the local airport, and plane B is ascending from the same airport. Plane A is descending at a rate of 2,500 feet perminute. Plane B is ascending at a rate of 4,000 feet per minute. If plane A is currently at an altitude of 14,000 feet and plane B is at an altitude of1,000 feet, how long will it take them to be at the same altitude? Represent time in minutes as the x-variable and altitude in thousands of feet asthe y-variable.
Let:
y1 = altitude of the plane A
y2 = altitude of the plane B
Let's find the equation for plane A:
[tex]\begin{gathered} m1=-2500 \\ y1=-2500x+b \\ for \\ 14000=-2500(0)+b \\ b=14000 \\ y1=-2500x+14000 \end{gathered}[/tex]And for plane B:
[tex]\begin{gathered} m2=4000 \\ y2=4000x+b \\ for \\ 1000=4000(0)+b \\ b=1000 \\ y2=4000x+1000 \end{gathered}[/tex]So:
[tex]\begin{gathered} y1=y2 \\ -2500x+14000=4000x+1000 \\ solve_{\text{ }}for_{\text{ }}x\colon_{} \\ 6500x=13000 \\ x=\frac{13000}{6500} \\ x=2 \end{gathered}[/tex]Answer:
2 minutes
List the side lengths of △TUV in order from smallest to largest.
The sum of angles in a triangle is 180°
From the given angles given, if we are to determine the sizes of the angles from least to the highest, we will simply add the angles together and then equate to 180°
Solution
[tex](P+60)+(44P)+(P+74)=180[/tex][tex]\begin{gathered} 2P+44P+134=180 \\ 46P=180-134 \\ 46P=46 \\ P=\frac{46}{46} \\ P=1 \end{gathered}[/tex]The next step will be to find the values of each angle
[tex][tex][tex]Since we have the values of each angle of the triangles, we can list out the sides of the triangles from smallest to largest
we will have
The smallest to be UV
The bigger will be UT
The biggest will be TV
Thus, the order is
[tex]UVWhich is the best buy?3-kilogram bag of lollipops for $10.505-kilogram bag of lollipops for $18.672-kilogram bag of lollipops for $9.224-kilogram bag of lollipops for $12.64
Given
3-kilogram bag of lollipops for $10.50
5-kilogram bag of lollipops for $18.67
2-kilogram bag of lollipops for $9.22
4-kilogram bag of lollipops for $12.64
Required
we need to find which among these is the best buy.
Explanation
For 3-kilogram bag for $10.50
[tex]\text{ cost of 1 kg bag=}\frac{10.50}{3}=3.5[/tex]For 5-kilogram bag of lollipops for $18.67
[tex]\text{ cost of 1 Kg bag=}\frac{18.67}{5}=3.73[/tex]for 2-kilogram bag of lollipops for $9.22
[tex]\text{ cost of 1 Kg bag=}\frac{9.22}{2}=4.61[/tex]for 4-kilogram bag of lollipops for $12.64
[tex]\text{ cost of 1 Kg bag =}\frac{12.64}{4}=3.16[/tex]Here the minimum cost per kg is for 4-kilogram bag of lollipops for $12.64. So it is the best buy.
x = 23 is a solution for the equation x/2 = 10 true or false
False
Here, we want to check if x = 23 is a solution for the equation
Firstly, we need to understand that what we have is a linear equation, an equation in which the highest power of the variable is 1. For this type of equations, what we expect is a single solution.
Thus;
[tex]\begin{gathered} \frac{x}{2}\text{ = 10} \\ \\ x\text{ = 2 }\times\text{ 10} \\ \\ x\text{ = 20} \end{gathered}[/tex]Since x = 20 is the only possible solution, then x = 23 as a solution must be incorrect and false
The amount of medication in a patient's bloodstream decreases exponentially from the time the medication is administered. For a particular medication, a function that gives the amount of medication in Use this a patient's bloodstream t hours after taking a 100 mg function to find the amount of medication remaining after 2 hours. 39 mg 59 mg 49 mg 29 mg 1 2 3 4 5 28
Let's solve the function for when t = 2
[tex]\begin{gathered} A(2)=100(\frac{7}{10})^2 \\ A(2)=100\cdot\frac{7^2}{10^2} \\ A(2)=100\cdot\frac{49}{100} \\ A(2)=49 \end{gathered}[/tex]The answer would be 49mg
Find the greatest common factor of the following function 15x3+9x2-30x
ok
[tex]undefined[/tex]1.1. Which statement explains why the two systems of equations below have thesame solution?A6x + 8y = -102x - 5y = 12B8x + 3y = 212x + 16y = -20
Let:
[tex]\begin{gathered} 6x+8y=-10_{\text{ }}(1) \\ 2x-5y=12_{\text{ }}(2) \\ 8x+3y=2_{\text{ }}(3) \\ 12x+16y=-20_{\text{ }}(4) \end{gathered}[/tex][tex]\begin{gathered} (4)=2(1) \\ so\colon \\ 2(6x+8y)=2(-10)\equiv12x+16y=-20 \\ 12x+16y=-20\equiv12x+16y=-20 \end{gathered}[/tex]Therefore, (4) is a Scalar Multiple of (1).
[tex]\begin{gathered} (1)+(2) \\ 6x+2x+8y-5y=-10+12 \\ 8x+3y=2\equiv(3) \\ so\colon_{} \\ (1)+(2)\equiv(3) \end{gathered}[/tex]Therefore, (3) is a linear combination of (1) and (2)
Question 3 of 10Which of the following are exterior angles? Check all that apply.
The possible angles are exterior angles:
[tex]\measuredangle2,\text{ }\measuredangle4\text{ and }\measuredangle6[/tex]The inner angles of the triangle are:
[tex]\measuredangle5\text{ and }\measuredangle1[/tex]We also can see that:
[tex]\measuredangle1\text{ }\cong\measuredangle3\text{ and }\measuredangle2\text{ }\cong\measuredangle4[/tex]Since
[tex]\measuredangle1\text{ and }\measuredangle3\text{ }[/tex]They are vertical angles formed by two intersecting lines, and 1 is congruent to 3. So, 3 is a