Directed line segment DE has endpoints D(-4,-2) and E(1,8). Point F divides DE such that DF:FE is 3:2What are the coordinates of F?
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The Solution.
The given points are
[tex]D(-4,-2)\text{ and E(1,8)}[/tex]The formula is
[tex]\frac{mx_2+nx_1}{m+n}_{},\frac{my_2+ny_1}{m+n}[/tex]In this case,
[tex]m=3,n=2[/tex]Therefore,
[tex]\begin{gathered} (\frac{mx_2+nx_1}{m+n}_{},\frac{my_2+ny_1}{m+n}) \\ =(\frac{3(1)+_{}2(-4)_{}}{3+2}_{},\frac{3(8)_{}+2(-2)_{}}{3+2}) \\ \end{gathered}[/tex][tex]=(\frac{3-8}{5},\frac{24-4}{5})=(-\frac{5}{5},\frac{20}{5})[/tex][tex]=(-1,4)[/tex]Hence, the correct answer is (-1, 4) (option 3)
Related Questions
m is the perpendicular bisector of ab find the value of x
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Given:
m is the bisector of AB
In a triangle ADC,
[tex]DC^2=(6x-25)^2-83^2\ldots\text{ (1)}[/tex]In a triangle BDC
[tex]DC^2=(3x+77)^2-83^2\ldots\text{ (2)}[/tex]From equation(1) and (2),
[tex]\begin{gathered} (6x-25)^2-83^2=(3x+77)^2-83^2 \\ 6x-25=3x+77 \\ 3x=77+25 \\ 3x=102 \\ x=34 \end{gathered}[/tex]The following two-way table describes student'safter school activities. Find the probability that arandomly selected student is in music/drama.Grade SportsMusic/DramaWorkSophomore2073Junior20132Senior2555P(Music/Drama) = [?]Round to the nearest hundredth.
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The two way table shows the following totals;
[tex]\begin{gathered} Sports=65 \\ \text{Music / Drama=25} \\ \text{Work}=10 \end{gathered}[/tex]The probability that a randomly selected student is in music/drama therefore is;
[tex]\begin{gathered} P\lbrack E\rbrack=\frac{Number\text{ of required outcomes}}{Number\text{ of all possible outcomes}} \\ P\lbrack\text{ music/drama\rbrack=}\frac{25}{100} \\ P\lbrack\text{ music/drama\rbrack=0.25} \end{gathered}[/tex]what is the transformation of [tex]g(x) = 4 - {x}^{3} [/tex]
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Given the transformed function:
[tex]g(x)=4-x^3[/tex]We want to describe the transformation with respect to the parent function:
[tex]f(x)=x^3[/tex]The "negative" in front of x^3 makes the graph reflect about x -axis.
Then, we have another transformation. There is a "+4" at the beginning.
This shifts the graph 4 units up.
Thus, the function f(x) is transformed to g(x) by:
• Shifting 4 units up
,• being reflected about the x-axis
We can show the graph of both the functions.
[tex]\begin{gathered} f(x)=x^3 \\ g(x)=4-x^3 \end{gathered}[/tex]Parent function is the red one.
Transformed function, g(x), is the blue one.
solve each inequality. Graph and check your solution. (if no solution write no solution if all real numbers write all real numbers.)5n + 3 > equal to 7(n-3)6 - 2p > equal to -33 (y - 4) < 5 (y + 2)
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The first given inequality is
[tex]5n+3\ge7(n-3)[/tex]First, we use the distributive property
[tex]5n+3\ge7n-21[/tex]Second, we subtract 7n on each side
[tex]\begin{gathered} 5n+3-7n\ge7n-21-7n \\ -2n+3\ge-21 \end{gathered}[/tex]Third, we subtract 3 on each side
[tex]\begin{gathered} -2n+3-3\ge-21-3 \\ -2n\ge-24 \end{gathered}[/tex]At last, we divide the inequality by -2, which changes the inequality sign
[tex]\begin{gathered} \frac{-2n}{-2}\leq\frac{-24}{-2} \\ n\leq12 \end{gathered}[/tex]Therefore, the solution is all real numbers less than or equal to 12.
We repeat the process for the other inequalities.
[tex]\begin{gathered} 6-2p\ge-3 \\ 6-2p-6\ge-3-6 \\ -2p\ge-9 \\ \frac{-2p}{-2}\leq\frac{-9}{-2} \\ p\leq\frac{9}{2} \end{gathered}[/tex]The solution is all real numbers less than or equal to 9/2.
The last inequality would be
[tex]\begin{gathered} 3(y-4)<5(y+2) \\ 3y-12<5y+10 \\ 3y-12-5y<5y+10-5y \\ -2y-12<10 \\ -2y-12+12<10+12 \\ -2y<22 \\ \frac{-2y}{-2}>\frac{22}{-2} \\ y>-11 \end{gathered}[/tex]The solution is all real numbers greater than -11.
At the train station, the cost for parking is based on an hourly fee. Patrons that park for 2 hours or less are charged at the short termparking fee but patrons that park for more than 2 hours are charged at the long term parking fee. The parking cost can be modeledwith the following piecewise equation, where x represents the number of hours.f(x) = {12x, x ≤ 2 15x, x > 2How much would it cost to park at the train station for 7 hours?Enter your answer in the box.$
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We have a fee that is modeled by the piecewise function:
[tex]f(x)=\begin{cases}12x,x\le2 \\ 15x,x>2\end{cases}[/tex]We have to find the total fee for x = 7 hours.
As x = 7 > 2, we use the second part of the function, 15x.
Then, we can calculate the fee as:
[tex]f(7)=15(7)=107[/tex]Answer: $107
can you find the slope for, (5,-3) & (10,-6) ?
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EXPLANATION:
To find the slope we must use the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Now we must identify at the given points which correspond to x and which to y; and then we must replace them in the slope formula;
Points: ( 5, -3) and (10, -6)
x1 y1 x2 y2
Now we replace;
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ m=\frac{-6-(-3)}{10-5} \\ m=\frac{-3}{5} \\ \text{ANSWER: The slope is m=}\frac{-3}{5} \end{gathered}[/tex]calculate the slope between the two points given (9,-2) (6,4)
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We have the next formula to calculate the slope between two points
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) is one point and the other point is (x2,y2)
in our case
(9,-2)=(x1,y1)
(6,4)=(x2,y2)
we substitute the values in the formula
[tex]m=\frac{4+2}{6-9}=\frac{6}{-3}=-2[/tex]the slope is -2
Using HL, are the two triangles congruent? What information would be used?Answers on imagine
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Given two triangles belowUsing
Using H and L as the base corner, then it can be observed that
[tex]LM\cong HJ(\text{given)}[/tex][tex]MN\cong JI(\text{given)}[/tex][tex]NL\cong IH(same\text{ side)}[/tex]Since each sides of the two triangles are are equal, therefore, triangles LMN is congruents to triangle HJL
Hence, the final is
Yes, the triangles are congruent by HL, line IJ ≅ NM, line LM ≅ HJ, OPTION D
Elizabeth brought a box of donuts to share. There are two-dozen (24) donuts in the box, all identical in size, shape, and color. Five are jelly-filled, 4 are lemon-filledand 15 are custard-filled. You randomly select one donut, eat it, and select another donut Find the probability of selecting two lemon-filled donuts in a row.Type an integer get or a simplified fraction
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We need to find the probability of selecting two lemon-filled donuts in a row.
That probability is the product of the following:
• the probability of selecting one of the ,4, lemon-filled donuts ,out of 24, donuts (first selection);
• the probability of selecting one of the ,3, lemon-filled donuts that are left ,out of 23, donuts (second selection, after you eat one lemon-filled donut);
Since, in the beginning, there are 4 lemon-filled donuts, and a total of 24 donuts, the probability of selecting a lemon-filled donut the first time is:
[tex]\frac{4}{24}=\frac{1}{6}[/tex]Now, given that the first selected one was a lemon-filled donut (eaten by you), there are left only 3 lemon-filled donuts, and a total of 23 donuts.
Thus, the probability of selecting a lemon-filled donut the second time (given you selected a lemon-filled donut the first time) is:
[tex]\frac{3}{23}[/tex]Therefore, the probability of selecting two lemon-filled donuts in a row is given by:
[tex]\frac{1}{6}\cdot\frac{3}{23}=\frac{3}{6}\cdot\frac{1}{23}=\frac{1}{2}\cdot\frac{1}{23}=\frac{1}{2\cdot23}=\frac{1}{46}[/tex]Thus, the answer is:
[tex]\frac{1}{46}[/tex]I need help better understanding functions
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The correct answer is option 2;
Not a function.
A relation can only be a function when every single x values have exactly one corresponding y value.
Observe that along the x-axis, two of the points are shown with the ordered pairs;
[tex](-2,0),(6,0)[/tex]This means, when x is negative 2, y is 0. Also when x is 6, y is 0.
For this reason, the graph is not a function. The values of y = 0 has two different x values
A painting of fruit has 5 pairs and a apples enable what is the ratio of apples to total fruit
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Number of pears = 5
Number of apples = 8
Total number of fruit = 5 + 8 = 13
Ratio apples to total fruit = 8/13
macy ran 11.2 miles in 4 days he ran the same distance every day how far did he jog every day
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If she jog the same distance every day, then we can divide the total miles in the number of days so:
[tex]\frac{11.2}{4}=2.8[/tex]This means that she jog 2.8 miles every day
What is the volume of the volleyball? Round answers to the nearest 10th and use 3.14 for pi
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Explanation
Given the diameter of the sphere as
[tex]d=10\text{ inches}[/tex]We can find the volume of the sphere using the formula below;
The formula for the volume of a sphere is given as;
[tex]\begin{gathered} V=\frac{4}{3}\pi r^3 \\ V=\frac{4}{3}\times3.14\times10^3 \\ V=4186.7 \end{gathered}[/tex]Answer: 4186.7 cubic inches
how do you subtract powers , for example 9.7 x 10 to the power of 5 minus 8.73 x 10 to the power of 5?
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Solution:
Given:
[tex](9.7\times10^5)-(8.73\times10^5)[/tex]To subtract the numbers, since they both have the same power, we subtract the decimal numbers separately and multiply by the number having the exponents.
Hence,
[tex]9.7-8.73=0.97[/tex]Now multiply by 10 to the power of 5.
Therefore, the final answer is;
[tex]\begin{gathered} 0.97\times10^5 \\ \\ In\text{ standard form;} \\ 9.7\times10^4 \end{gathered}[/tex]Middle school problem, Please explain very well or don't answer it.
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Dante lost 35 pennies.
Mia lost 315 pennies; from the piggy bank.
What is defined as the fraction?Proper fractions are those whose numerator is smaller than the denominator. Proper fractions include 5/7, 3/8, 2/5, and the like.Unit fractions are fractions with a numerator of one. For instance, 1/4, 1/7, and so on.For the given question.
Let Dante have total amount of x.
Then, Mia has the amount if 350 - x.
Dante lost 1/2 of his pennies = x - (1/2)x = (1/2)x.
Mia lost 1/3 of her pennies and left pennies is = (1/3)(350 - x)
Now, both had the same number of pennies.
(1/2)x = (1/3)(350 - x)
cross multiplying.
3x = 2(350 - x)
3x = 350 - 2x
5x = 350
x = 70 (Dante have 70 number of pennies)
Dante lost = (1/2)x = 70/2 = 35 pennies.
Mia lost = (1/3)(350 - x) = 315 pennies.
To know more about the fraction, here
https://brainly.com/question/1136789
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Which of the following integrals cannot be evaluated using a simple substitution? (4 points) Select one:a. the integral of the square root of the quantity x minus 1, dxb. the integral of the quotient of 1 and the square root of the quantity 1 minus x squared, dxc. the integral of the quotient of 1 and the square root of the quantity 1 minus x squared, dxd. the integral of x times the square root of the quantity x squared minus 1, dx
Answers
Given:
There are given that the integral:
[tex]\int_{-8}^8\sqrt{64-x^2}dx[/tex]Explanation:
From the given integral;
[tex]\int_{-8}^8\sqrt{64-x^2}dx[/tex]Now,
Apply the trigonometry rule that is:
[tex]\int_{-a}^a\sqrt{b-x^2}dx=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}bcos^2(u)du[/tex]Then,
From the function:
[tex]\int_{-8}^8\sqrt{64-x^2}dx=\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}64cos^2udu[/tex]Then,
Take the constant out:
So,
[tex]\begin{gathered} \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}64cos^2udu=64\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}cos^2udu \\ =64\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}\frac{1+cos2u}{2}du \\ =\frac{64}{2}\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}1+cos2udu \end{gathered}[/tex]Then,
[tex]\begin{gathered} \frac{64}{2}\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}1+cos2udu=32\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}1du+\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}}cos2udu \\ =32(\pi+0) \\ =32\pi \end{gathered}[/tex]Final answer:;
Hence, the correct option is C.
I need help solving for x and Y can someone please help me
Answers
Answer: The solution is (1, 2)
Explanation:
The given equations are
5x - 4y = - 3
x - 6y = - 11
We would apply the method of substitution. From the second equation, if we add 6y to both sides, it becomes
x - 6y + 6y = 6y - 11
x = 6y - 11
We would substitute x = 6y - 11 into the second equation. It becomes
5(6y - 11) - 4y = - 3
By expanding the parentheses, it becomes
30y - 55 - 4y = - 3
By collecting like terms, we have
30y - 4y = - 3 + 55
26y = 52
Dividing both sides by 26, we have
26y/26 = 52/26
y = 2
Substituting y = 2 into x = 6y - 11, we have
x = 6(2) - 11
x = 12 - 11
x = 1
The solution is (1, 2)
What is the equation for this situation? The table shows a representation of the number of miles a car drives over time. Hours, Miles, y Which could NOT be a point on this table? 3 195 4 260 5 325 6 390 Pattern: Eachx value is multiplied by 65 to get each y value.
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To find the equation, first, we have to find the ratio of change which is the slope.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing the points (3,195) and (5,325), we have
[tex]m=\frac{325-195}{5-3}=\frac{130}{2}=65[/tex]Once we have the slope, we use one point and the point-slope formula to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-195=65(x-3) \\ y-195=65x-195 \\ y=65x-195+195 \\ y=65x \end{gathered}[/tex]Therefore, the equation is y = 65x.
All the points on the table must follow the pattern or equation. A point that shouldn't be on the table is (8,455) because if you multiply 8 times 65 you get 520, not 455.
Therefore, a point that couldn't be on this table is (8,455).
Simplify to determine the number of solutions 8(5b+3)=10(4b+2)
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We will solve as follows:
[tex]8(5b+3)=10(4b+2)\Rightarrow40b+24=40b+20[/tex][tex]\Rightarrow40b-40b=20-24\Rightarrow0\ne-4[/tex]The problem has no real solutions.
Answer:
no solution
Step-by-step explanation:
8(5b + 3) = 10(4b + 2) ← distribute parenthesis on both sides
40b + 24 = 40b + 20 ( subtract 24 from both sides )
40b = 40b - 4 ( subtract 40b from both sides )
0 = - 4 ← not possible
this indicates the equation has no solution
what is 14/15 ÷7 with an estimate
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we have the following:
[tex]\frac{\frac{14}{15}}{\frac{7}{1}}=\frac{1\cdot14}{15\cdot7}=\frac{14}{105}[/tex]therefore, the answer is 14/105 = 0.133
pierre drew a picture of a tree he plans to draw the same picture after a transformationfor which which type of transformation will the tree appear upside down?
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The tree will appear upside down after a reflection over an horizonatal line.
a 90° degree rotation will only make the tree appear horizontally.
A 360 degree ratotaion will end with the tree in the same position,
find an angle between 0 and 2π that is coterminal with 33π/10
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The Solution.
Coterminal angles are angles that differ by a whole number of complete circles.
So, The coterminal angles of the given angle in the interval [0,2pi} is obtained as below:
[tex]\frac{33\pi}{10}-2\pi=3\frac{3\pi}{10}-2\pi=1\frac{3}{10}\pi[/tex]Thus, the coterminal angle within the given range is
[tex]1\frac{3}{10}\pi\text{ or }\frac{13}{10}\pi[/tex]Suppose cot(theta) = -8/7 and theta is in quadrant 4. find the value of csc(theta).
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Since we already know of the measure for the opposite side, we need to solve for the hypotenuse using Pythagorean theorem
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=(-7)^2+(8)^2 \\ c^2=49+64 \\ c^2=113 \\ \sqrt[]{c^2}=\sqrt[]{113} \\ c=\sqrt[]{113} \end{gathered}[/tex]Now that we know the measure of the hypotenuse, substitute it to the definition for cosecant and we have
[tex]\begin{gathered} \csc \theta=\frac{\text{hypotenuse}}{\text{opposite}} \\ \csc \theta=\frac{\sqrt[]{113}}{-7} \\ \\ \text{Therefore} \\ \csc \theta=-\frac{\sqrt[]{113}}{7} \end{gathered}[/tex]A student receives scores of 85, 78 and 81 on his first 3 exams in algebra. What is the lowest score the student has to get on his fourth exam, so his test average would be at least an 84?
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The student's scores in his first three exams are 85, 78, and 81.
You have to find what score is needed on a fourth exam to have an average grade of at least 84 points.
To determine the average score of 4 exams, you have to add each score and divide it by the number of exams, following the formula:
[tex]\bar{X}=\frac{\sum ^n_1x_i}{n}[/tex]Where
xi represents each observation of the sample, in this exercise, it represents the score of each test.
n represents the same size, in this exercise, is the number of algebra tests
We know that:
The average is 84 points
n= 4 tests
Three observations are 85, 78, 81
If "x" represents the score of the fourth Test, then the calculation of the average grade can be expressed as:
[tex]84=\frac{85+78+81+x}{4}[/tex]From this expression, you can determine the value of x
-Solve the sum on the denominator:
[tex]84=\frac{244+x}{4}[/tex]-Multiply both sides by 4
[tex]\begin{gathered} 84\cdot4=4\cdot\frac{244+x}{4} \\ 336=244+x \end{gathered}[/tex]-Subtract 244 from both sides
[tex]\begin{gathered} 336-244=244-244+x \\ 92=x \end{gathered}[/tex]This means that the student needs at least 92 points on the fourth test, for his average score to be at least 84 points.
Let f(x) = 2x – 1 and g(x) = 3x Find f(g(- 3))
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
f(x) = 2x – 1
g(x) = 3x
f(g(- 3)) = ?
Step 02:
f(g(x)) = 2(3x) - 1
= 6x - 1
f(g(- 3)) = 6(-3) - 1
= -18 - 1
= -19
The answer is:
f(g(- 3)) = -19
Use the points (7,69) and (12,34) from the following data set to determine the point slope form of an equation that represents the data set.
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Given:
Point are (7,69) and (12,34)
So the slope is:
[tex]\begin{gathered} m=\text{slope } \\ m=\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)=\text{ First point} \\ (x_2,y_2)\text{ = second point} \end{gathered}[/tex]Here:
[tex]\begin{gathered} x_1=7 \\ y_1=69 \\ x_2=12 \\ y_2=34 \end{gathered}[/tex][tex]\begin{gathered} m=\frac{34-69}{12-7} \\ m=\frac{-35}{5} \\ m=-7 \end{gathered}[/tex]Equation of line:
[tex]\begin{gathered} y=mx+c \\ (7,69) \\ 69=-7(7)+c \\ c=118 \end{gathered}[/tex][tex]\begin{gathered} y=mx+c \\ y=-7x+118 \end{gathered}[/tex]Davis is an architect earning $148,800 a year. He ismarried and is paid on a biweekly basis. How much is withheldfrom each paycheck for state taxes
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for this we must divide by the number of fortnights that the year has
one month has 2 fortnights so 12 months have 24 fortnights
[tex]\frac{148800}{24}[/tex][tex]=6200[/tex]so he earns $6,200 biweekly basis
Hello! I need some assistance with this homework question for precalculus, please?HW Q20
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According to the logarithm definition:
[tex]\log_bc=a\Leftrightarrow b^a=c[/tex]In this question:
[tex]\begin{gathered} 3.6=6^x \\ which\text{ }is\text{ }the\text{ }same\text{ }as \\ 6^x=3.6 \end{gathered}[/tex]Then, comparing with the definitionm:
a = x
b = 6
c = 3.6
And, transforming to the log form:
[tex]\begin{gathered} \begin{equation*} \log_bc=a \end{equation*} \\ \log_6(3.6)=x \end{gathered}[/tex]Answer:
[tex]\operatorname{\log}_{6}(3.6)= x[/tex]Find the solution set of the inequality 15x-14<-29
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Then, the solution of the equation is x<-3. This can also be writen in terms of intervals as
[tex](-\infty,-3)[/tex]Jake is enclosing a rectangular field that is 47 yards by 158 yards with wood fencing. The cost per foot of wood fencing is $3.28.How much will the wood fencing cost?A $672.40B. $1.344.80C $2,017.20D. $4,034.40
Answers
Let's begin by listing out the given information:
Width (w) = 47 yards = 141 ft
Length (l) = 158 yards = 474 ft
Cost (c) = $3.28 /ft
We will calculate the Perimeter of the field. We have:
[tex]\begin{gathered} P=2(l+w) \\ P=2(474+141)=2(615) \\ P=1230ft \end{gathered}[/tex]The cost for this is given by:
[tex]\begin{gathered} C=P\times c \\ C=1239\times3.28 \\ C=\text{\$}4034.40 \end{gathered}[/tex]Therefore, the correct answer is D ($4,034.40)