We want to find the equation of the line that passes through the points:
(4 , -8) and (9 , 11)
First, we're going to find the slope between these points using the fact that:
If we have two points that lie on a line:
[tex](x_1,y_1)\text{ and }(x_2,y_2)[/tex]The slope between them can be found using the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]If we replace our values:
[tex]\begin{gathered} (x_1,y_1)=(4,-8) \\ (x_2,y_2)=(9,11) \\ x_1=4 \\ x_2=9 \\ y_1=-8 \\ y_2=11 \end{gathered}[/tex]The slope will be:
[tex]m=\frac{11-(-8)}{9-4}=\frac{11+8}{5}=\frac{19}{5}[/tex]Now, we could apply the point-slope equation. This equation tells us that we can find the equation of the line if we got a point (x1,y1) on the line, and the slope m:
[tex]y=y_1+m(x-x_1)[/tex]Replacing our values:
[tex]\begin{gathered} y=-8+\frac{19}{5}(x-4) \\ y=-8+\frac{19}{5}x-\frac{76}{5} \\ y=\frac{19}{5}x-\frac{116}{5} \end{gathered}[/tex]This, is the general form. We want to express the last equation as a standard form like this:
[tex]Ax+By=C[/tex]If we re-write:
[tex]\begin{gathered} y=\frac{19x-116}{5} \\ \\ 5y=19x-116 \\ 19x-5y=116 \end{gathered}[/tex]Therefore, the standard for the equation of the line that passes through (4 , -8) and (9, 11) is:
19x-5y=116
MAKE CONNECTIONSKatie is twice as old as her sister Mara. The sum of their ages is 24. Write a one-variable equation tosituation
Answer
3x = 24
Explanation
Let sister Maria's age be represented by x.
Katie is twice as old as her sister Mara
So Katie's age will be 2x.
If the sum of their ages is 24, it implies x + 2x =24
Therefore, a one-variable equation to the situation will be: 3x = 24
At the North Carolina Zoo there is a bucket that contains food for the gorillas and the grizzly bears. The gorilla food weighs 5.384 kg. The gorilla food weighs 0.796 kg more than the grizzly bear food. How much food for both gorillas and grizzly bears are in the bucket?
The food for both gorilla and grizzly bear in the bucket is 9.972 kg.
Given, at the North Carolina Zoo there is a bucket that contains food for the gorillas and the grizzly bears.
The gorilla food weighs 5.384 kg. The gorilla food weighs 0.796 kg more than the grizzly bear food.
Let the weight of the grizzly bear food be x,
According to the question,
weight of gorilla food = weight of grizzly bear food + 0.796 kg
5.384 = x + 0.796
x = 5.384 - 0.796
x = 4.588
So, the food for both gorilla and grizzly bear in the bucket is 9.972 kg.
Hence, the food for both gorilla and grizzly bear in the bucket is 9.972 kg.
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which property of equality was used?3m + 14 = 193m + 14 - 14 = 19 - (19 - 5)
ANSWER
Subtraction property of equality
EXPLANATION
In this problem they subtracted 14 from both sides of the equation. On the left side we can see that subtraction clearly, but on the right side, we have (19-5). If we solve this: 19 - 5 = 14, we can see that 14 has been subtracted from the right side too.
An object projected upwards with a velocity of 96 feet per second from a height of 6 feet above theground is modelled by the function ℎ() = −162 + 96 + 6 .A. [3 pts] How many seconds after launch will the object reach its maximum height? Round your answerto one decimal place.B. [3 pts] Find the maximum height that the object reaches. Round your answer to one decimal place.C. [3 pts] Find the x-intercept and explain its meaning on the context of the problem.D. [3 pts] After how many seconds will the object be 100 feet above the ground?E. [2 pts] Find the y-intercept and explain its meaning on the context of the problem
Given:
[tex]h(t)=-16t^2+96t+6[/tex]Find-:
(a) Maximum second after launch will the object reach its maximum height
(b) Find the maximum height that the object reaches.
(c) Find the x-intercept and explain its meaning in the context of the problem.
(d) After how many seconds will the object be 100 feet above the ground
(e) Find the y-intercept and explain its meaning on the context of the problem
Sol:
(a)
Maximum second after launch.
For maximum value derivative should be zero.
[tex]\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ h^{\prime}(t)=-(16\times2)t+96 \\ \\ \end{gathered}[/tex][tex]\begin{gathered} -32t+96=0 \\ \\ 32t=96 \\ \\ t=\frac{96}{32} \\ \\ t=3 \end{gathered}[/tex]After 3-second the object reaches maximum height.
(b)
For maximum height is at t = 3
[tex]\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ h(3)=-16(3)^2+96(3)+6 \\ \\ h(3)=(-16\times9)+(96\times3)+6 \\ \\ h(3)=-144+288+6 \\ \\ =150 \end{gathered}[/tex](c) x-intercept the value of y is zero that means:
[tex]\begin{gathered} h(t)=0 \\ \\ -16t^2+96t+6=0 \\ \\ -8t^2+48t+3=0 \\ \\ t=\frac{-48\pm\sqrt{48^2-4(-8)(3)}}{2(-8)} \\ \\ t=\frac{-48\pm48.98}{-16} \\ \\ t=6;t=-0.061 \end{gathered}[/tex]The negative value of "t" is not considered so at
x-intercept is 6 and -0.061
(d) Object be 100 feet above grounded is:
[tex]\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ -16t^2+96t+6=100 \\ \\ -16t^2+96t-94=0 \\ \\ -8t^2+48t-47=0 \\ \end{gathered}[/tex]So, the time is:
[tex]\begin{gathered} t=\frac{-48\pm\sqrt{48^2-4(-8)(-47)}}{2(-8)} \\ \\ t=\frac{-48\pm\sqrt{800}}{-16} \\ \\ t=\frac{-48-28.28}{-16},t=\frac{-48+28.28}{-16} \\ \\ t=4.76,t=1.23 \end{gathered}[/tex]At t= 4.76 and t =1.23
(e)
For y-intercept value of "x" is zero.
[tex]\begin{gathered} h(t)=-16t^2+96t+6 \\ \\ h(0)=-16(0)^2+96(0)+6 \\ \\ h(0)=6 \end{gathered}[/tex]So, the y-intercept is 6.
A certain forest covers an area of 2300 km^2. Suppose that each year this area decreases by 7.75%. What will the area be after 8 years?Use the calculator provided and round your answer to the nearest square kilometer.
EXPLANATION:
Given;
We are told that a forest covers an area of 2300 square kilometers.
Next we are told that this forest area decreases by 7.75% each year.
Required:
We are required to calculate the area remaining after 8 years.
Step-by-step solution:
To solve this math problem, take note that what we have is an exponential decay problem. The initial size decreases (decays) at a constant rate every year.
The formula for an exponential growth/decay is given as shown below;
[tex]f(x)=a(1-r)^x[/tex]Where the variables are as follows;
[tex]\begin{gathered} a=initial\text{ }value \\ r=rate\text{ }of\text{ }decay \\ x=number\text{ }of\text{ }years \end{gathered}[/tex]With the values given, we can substitute and we'll have the following;
[tex]f(8)=2300(1-0.0775)^8[/tex][tex]f(8)=2300(0.9225)^8[/tex][tex]f(8)=2300(0.524482495947)[/tex][tex]f(8)=1206.3097...[/tex]Rounded to the nearest square kilometer, we would now have;
ANSWER:
[tex]Area\text{ }after\text{ }8\text{ }years=1206km^2[/tex]Determine whether the following is a trinomial square.x² - 8x + 64-O NoYes
A trinomial square has two possible forms:
[tex]\begin{gathered} (a+b)^2=a^2+2ab+b^2 \\ (a-b)^2=a^2-2ab+b^2 \end{gathered}[/tex]So, for us to check if
[tex]x^2-8x+64[/tex]Is a trinomial square, we first check if the first and thrid terms are positive, because both options has positive first and thrid terms, even if a or b are negative, because they are squared in the process.
Both are positive, x² and 64.
Now, by comparison, we see that, in thi case we would have:
[tex]\begin{gathered} a=x \\ b^2=64 \\ b=8 \end{gathered}[/tex]If it is a trinomial square, than the middle term has to be:
[tex]-2ab[/tex]We use the negative form because we have a negative middle term.
So, let's see if it checks out:
[tex]-2ab=-2x\cdot8=-16x[/tex]We got -16x, but the middle term is -8x, they don't match.
Since they don't match, the given expression is not a trinomial square. The answer is No.
Archanged2. A student used a random number generator with the digits 1 to 20 to simulate the total number of questions she might guess correctly on atrue/false exam that had 20 questions. The dot plot below show the results of 100 trials.Based on the data, which number of correct answersmost likely, and what percentage of the 100 trials does this represent?Guessed 9 correctly on 30% of the trialsGuessed o correctly on 100% of the trialsGuessed 9 correctly on 25% of the trialsGuessed 10 correctly on 30% of the trials
The following observation are derived from the graph shown relating number of guesses against the number of trials
+) Guessed 6 correctly on 2% of the trials
+) Guessed 7 correctly on 8% of the trials
+) Guessed 8 correctly on 25% of the trials
+) Guessed 9 correctly on 30% of the trials
+) Guessed 10 correctly on 19% of the trials
+) Guessed 11 correctly on 12% 0f the trials
+) Guessed 12 correctly on 3% of the trials
+) Guessed 13 correctly on 1% of the trials
From the options provided, it can be concluded that:
He guessed 9 correctly on 30% of the trials. The first option is the correct option
Solve for q.
-18q+ 18q+ 2q + 14 = 4
q=
Answer:
-18q+18q+2q+14=4Step-by-step explanation:
Data:find "q'
first take 2 as common
solution .
2(-9q+9q+q+7)=4
Now divided 2 by both sides.
2(-9q+9q+q+7) ÷2
=4÷2
-9q+9q+q+7 =2
q+7=2
q=2-7
q=-5 Answer.
24. Cree la gráfica aproximada de la función cuadrática con intersecciones en x en (-5, 0) y (3,0) y una intersección en y en (0, -7.5). 1. Seleccione un botón para elegir el tipo de gráfico. 2. Arrastre los dos puntos a la posición correcta.
your budget is $80.00 to buy new clothes.what us the maximum whole dollar amount that you can spend on clothes, (bearing in mind that you will also have to pay 7.5 sales tax.)
We are told that the maximum amount to spend is $80 and that there is a 7.5% sales tax. If N is the amount we are going to spend then we need to have into account that we need to add the 7.5% of N and that should be at least equal to $80.
[tex]N+\frac{7.5}{100}N=80[/tex]Now we need to solve for N, to do that we add like terms:
[tex]\begin{gathered} (1+\frac{7.5}{100})N=80 \\ \frac{107.5}{100}N=80 \end{gathered}[/tex]Now we multiply both sides by 100:
[tex]107.5N=8000[/tex]Now we divide by 107.5:
[tex]N=\frac{8000}{107.5}[/tex]Solving the operations:
[tex]N=74.4\cong74[/tex]Therefore, the maximum amount to spend is $74
using the set of numbers find the mean rounded to the nearest tenth , median , mode and range.98 , 98 , 90 , 82 , 89 , 87
The median is defined as the sum of all the values divided by the total number of data, then in this case:
[tex]\begin{gathered} \mu=\frac{98+98+90+82+89+87}{6} \\ \mu=\frac{544}{6} \\ \mu=90.7 \end{gathered}[/tex]To find the median we need to order the data:
[tex]82,\text{ 87, 89, 90, 98, 98}[/tex]The median is the number that divides all the data in half, since we have an even number of data we need to take the mean between the middle data, that is, the median is:
[tex]\frac{89+90}{2}=89.5[/tex]The mode is the number that repeats itself more on the data set, then in this case we the mode is 98.
The range is the difference between the lowest and highest data, then:
[tex]98-82=16[/tex]Summing up we have:
mean: 90.7
median: 89.5
mode: 98
Range: 16
The table below represents a linear function f(x) and the equation represents a function (x)f(x)-1-12g(x)09(x) = 2x + 610Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x), (6 points)Part B: Which function has a greater y-intercept? Justify your answer (4 points)I
Answer:
(a)The slope of f(x) is greater than the slope of g(x).
(b)g(x) has a greater y-intercept.
Explanation:
Part A
From the table of f(x), we have the pairs:
(-1,-12),(0,-6) and (1,0).
First, we find the slope of f(x).
[tex]\begin{gathered} \text{Slope}=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}} \\ =\frac{-6-0}{0-1} \\ =-\frac{6}{-1} \\ =6 \end{gathered}[/tex]Given the function g(x) defined as follows:
[tex]g(x)=2x+6[/tex]Comparing g(x) with the slope-intercept form (y=mx+b), the slope of g(x) is m=2.
Sentence: The slope of f(x) is greater than the slope of g(x).
Part B
The y-intercept is the point in a function where x=0.
In f(x), When x=0, f(x)=-6
• The y-intercept of f(x) is -6.
Comparing g(x) with the slope-intercept form (y=mx+b), the y-intercept of g(x), b=6.
Therefore, g(x) has a greater y-intercept.
please help!!!!!!!!!!
plane flies 390 miles with the wind
or 325 miles against the wind
The speed of the wind is 10 miles per hour
find the speed of the plane
In this case, we can see that
[tex]\begin{gathered} \frac{390\text{ miles}}{x+10\text{ }}\text{ must be equal to } \\ \frac{325}{x-10} \end{gathered}[/tex]hence the answer is
[tex]\frac{390\text{ miles}}{x+10\text{ }}=\frac{325\text{ miles}}{x-10\text{ }}[/tex]Suppose that a certain fortunate person has a net worth of $76.0 billion ($ 7.60×1010 ). If her stock has a good year and gains $3.20 billion ( 3.20×109 ) in value, what is her new net worth? THE NEW NET WOTH IS 7.92×10^10 Suppose that this individual now decides to give one-eighth of a percent (0.125 % ) of her new net worth to charity. How many dollars are given to charity?
Find the 0.125% of 7.92x10^10: Multiply the amount by 0.125 and then divide into 100 or multiply the amount by 0.125/100
[tex]\begin{gathered} \frac{0.125}{100}=1.25\times10^{-3} \\ \\ 7.92\times10^{10}*1.25\times10^{-3}=(7.92*1.25)\times10^{10-3}=9.9\times10^7 \end{gathered}[/tex]Then, $9.9x10^7 are given to charity1 and In an experiment, the probability that event A occurs is –, the probability that event B occurs is 5 1 the probability that events A and B both occur is What is the probability that A occurs given that B occurs? Simplify any fractions. Submit
Solution
We have the following info given:
P(A) = 4/5
P(B)= 1/7
P(A and B) = 1/9
We want to find this probability:
P(A|B)= P(A and B)/P(B)
Replacing we got:
[tex]P(A|B)=\frac{\frac{1}{9}}{\frac{1}{7}}=\frac{7}{9}[/tex]
Identify the Sampling Method. Identify the sampling method (simple randomsampling, systematic sampling, convenience sampling, or stratified sampling) in the followingstudies. study of the use of antidepressants selects 50 participants between the ages of 20 and 29,50 participants between the ages of 30 and 39, and 50 participants between the ages of 40 and49.
Step 1
Analyze the Sampling method
In stratified sampling, the population is divided into two or more groups called strata according to some criterion such as geographic location, grade level, age, income, etc. Subsamples are randomly selected from each stratum. Elements within each stratum are homogenous but are heterogeneous across the strata. For example;
From this question, the general study is on the use of antidepressants. This is the strata, each stratum of 50 participants each based on age cuts across. They are homogenous in their individual stratum of age grades( 20-29), (30-39), (40-49) but are homogenous in the sense that 50 participants were chosen across all stratum and the study is generally about antidepressants.
Hence, the right answer is stratified sampling.
what is the value of x to the nearest tenth on problem 8
First let us define the theorem that would help us solve the problem
The two tangent theorem states that if we draw two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same.
Next, applying the theorem:
[tex]4x\text{ - 9 = 15}[/tex]Solving for x:
[tex]\begin{gathered} Collect\text{ like terms} \\ 4x\text{ = 15 + 9} \\ 4x\text{ = 24} \\ Divide\text{ both sides by 4} \\ \frac{4x}{4}\text{ = }\frac{24}{4} \\ x\text{ = 6} \end{gathered}[/tex]Answer:
x = 6
i need help with math Will u
The value of 'w' for the two parallel lines are cut by the transversal is 52.
What is meant by the supplementary angles?The term "supplementary angles" refers to a pair of angles which always add up to 180°. These two perspectives are known as supplements. When supplementary angles are combined, they form a straight angle (180 degrees). In other words, so unless Angle 1 + Angle 2 = 180°, angles 1 and 2 are supplementary.For the given question
Two parallel lines are cut by the transversal.
Then,
w + (3w -28) = 180 (same side exterior angle of the traversal are supplementary)
Solve the equation;
4w - 28 = 180
4w = 208
w = 208/4
w = 52
Thus, the value of 'w' for the two parallel lines are cut by the transversal is 52.
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Write the inequality shown by the shaded region in the graph with the boundary line 3x-y=9.
The equation given is,
[tex]3x-y=9[/tex]Since the boundary line is thick bold line and from the graph we can observe that the line (shaded portion) moves from the right to the left hand side.
Then the inequality of the shaded region is,
[tex]3x-y\leq9[/tex]anyone that knows about cos, tan, and csc please help!
Which part of the triangle do you feel most confident of identifying and why and How might you use a perpendicular bisector or an angle bisector in the everyday life.
Hello there. To solve this question, we have to remember some properties about triangles.
Given a triangle ABC as follows:
We can show for each point what it is on this triangle.
1. Midsegment. This is the segment that is parallel to the base, in this case BC and has half its length. Another property: it divides the sides AB and AC into proportional parts. See the drawing.
2. Circumcenter. Take the triangle and inscribe it in a circumference (all its vertices are in the circumference. Now take the perpendicular bisector of each sides. The point in which at least two of them intersects is the circumcenter. See the drawing.
3. Incenter. Take the bisectors of the angles of ABC. The point in which they intersect is the incenter. Another property: It is the center of the inscribed circumference that is tangent to all sides of the triangle.
In a recent survey of college-educated adults, 351 indicated that they regularly work more than 45hrs a week. If this represents 39% of those surveyed, how many people were in the survey?
Recall that the y% of x is given by the following expression:
[tex]x\cdot\frac{y}{100}\text{.}[/tex]Now, let S be the number of people that were in the survey, then, we know that 39% of S is 351, then we can set the following equation:
[tex]351=S\cdot\frac{39}{100}\text{.}[/tex]Multiplying the above equation by 100/39 we get:
[tex]\begin{gathered} 351\times\frac{100}{39}=S\cdot\frac{39}{100}\times\frac{100}{39}, \\ S=900. \end{gathered}[/tex]Answer: 900.
2(-6+-3)to the power of 2 - (-6+-4)
To solve this expression we need to solve the parenthesis first:
[tex]\begin{gathered} 2(-9)^{2-(-10)} \\ 2(-9)^{2+10} \\ 2(-9)^{12} \\ 2(282429536481)=564859072962 \\ \end{gathered}[/tex]harlyne deposited $3400 into a savings account that has an annual simple interest rate of 0.2%. Find the amount in the savings account after each number of years.
2 years $
5 years $
8 years $
The simple interest after 2, 5 and 8 years on a principal of $3400 at 0.2% are $3413.6, $3434 and $3454.4 respectively
SIMPLE INTERESTSimple interest is a quick and easy method to calculate interest on the money, in the simple interest method interest always applies to the original principal amount, with the same rate of interest for every time cycle.
Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r(%) and is to be written as r/100.
Principal: The principal is the amount that initially borrowed from the bank or invested. The principal is denoted by P.Rate: Rate is the rate of interest at which the principal amount is given to someone for a certain time, the rate of interest can be 5%, 10%, or 13%, etc. The rate of interest is denoted by R.Time: Time is the duration for which the principal amount is given to someone. Time is denoted by T.Amount: When a person takes a loan from a bank, he/she has to return the principal borrowed plus the interest amount, and this total returned is called Amount.Using the data given;
S.I = P × R × T
When T = 2 years
S.I = 3400 * 0.002 * 2
S.I = 13.6
The amount after 2 years = 3400 + 13. 6 = $3413.6
When T = 5 years
S.I = 3400 * 0.002 * 5
S.I = 34
The amount after 5 years = 34 + 3400 = $3434
When T = 8 years
S.I = $3454.4
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1. Given the points Al-1, 2) and B(7, 8), find the coordinates of the polnt P on the directed line segment JB that partitions AB in the ratio 1:3. Plot P along with segment AB. 10 B 6 (x,y) = (x1+k(x2 - x2),y. +k(y2-y) 2 210182632 2 68 110 2 24 6 8 -10 2. Find the coordinates of P so that P partitions AB in the ratio 5.1 with A(2, 4) and B(8, 10). L 3. Find the coordinates of P so that P partitions AB in the ratio 1 to 3 with A(-5, 4) and B(7,-4). 4. Find the coordinates of P so that P partitions AB in the ratio 3:4 with A(-9, -9) and B(5,-2).
We can find the point with help of the end points and the ratio so:
[tex]\begin{gathered} x=-1+\frac{1}{1+3}(7-(-1)) \\ x=-1+\frac{1}{4}8 \\ x=-1+2 \\ x=1 \end{gathered}[/tex]now for y:
[tex]\begin{gathered} y=2+\frac{1}{1+3}(8-2) \\ y=2+\frac{1}{4}6 \\ y=3.5 \end{gathered}[/tex]So now we can graph it so:
Find the length of FG, Express your answer as a fraction times pie.
Given:
EF = 2
m∠FEG = 144 degrees.
Let's fid the length of arc FG.
To find the length of arc FG, apply the formula:
[tex]L=2\pi r\times\frac{\theta}{360}[/tex]Where:
r is the radius = 2
θ is the central angle = 144 degrees.
Thus, we have:
[tex]\begin{gathered} L=2\pi\times2\times\frac{144}{360} \\ \\ L=4\pi\times\frac{2}{5} \\ \\ L=\frac{8}{5}\pi\text{ } \end{gathered}[/tex]Therefore, the length of arc FG as a fraction times pi is:
[tex]\frac{8}{5}\pi[/tex]ANSWER:
[tex]\frac{8}{5}\pi[/tex]1. Smoesnail crawls at 3/25 m.p.h. At this rate, how far can he get in 1 2/3 hours?
Answer:
[tex]\frac{1}{5}\text{ miles}[/tex]Explanation:
Here, we want to get the distance the snail can go in the given time
Mathematically, we have it that:
[tex]\text{Distance = sp}eed\text{ }\times\text{ time}[/tex]speed = 3/25 mph
Time = 1 2/3 hours = 5/3 hours
Thus, we have it that:
[tex]\text{Distance = }\frac{3}{25}\text{ }\times\frac{5}{3}\text{ = }\frac{1}{5}\text{ miles}[/tex]Which of the following is equivalent to the expression below? 196 - 54 +24
Given the follow:
Root96 - root54 + root24
We are to find the expression that is equivalent.
root96 = root16 x root6
root54 = root9 x root6
root24 = root4 x root6
(root16 x root6) - (root9 x root6) + (root4 x root6)
= 4root6 - 3root6 + 2root6
= (4 - 3 + 2)root6
= (1 + 2)root6
= 3root6
Therefore, the correct option is C which is 3root6
during the election of the last president 120 srudents voted fir Lindsey and 280 of the students voted for Sharif. 400 students total voted. What percentage voted for Lindsey
From a total of 400 students ,
120 votes for Lindsey
280 votes for Sharif
then 200 students = 50%
. 100 students= 25%
. 20 students = (50%)/10 = 5%
then 120 students (100+20) belows to 25%+5%= 30%
30% students voted for Lindsey
Can you provide an example of a number that is a perfect square
ANSWER
9
EXPLANATION
A perfect square is a number that can be expressed as the product of two equal integers.
For example, 9 is a perfect square because it can be expressed as the product 3 x 3 = 3² - which are two equal integers.