The value of x is [tex]x=\frac{-1+\sqrt{37}}{12}[/tex] and [tex]x=\frac{-1-\sqrt{37}}{12}[/tex]
Step-by-step explanation:
The equation is [tex]\frac{1}{x}-\frac{2}{3}=4 x[/tex]
Subtracting by [tex]4x[/tex] on both sides,
[tex]\frac{1}{x}-\frac{2}{3}-4 x=0[/tex]
Taking LCM,
[tex]\frac{3-12 x^{2}-2 x}{3 x}=0[/tex]
Multiplying by 3x on both sides,
[tex]-12 x^{2}-2 x+3=0[/tex]
Dividing by (-) on both sides,
[tex]12 x^{2}+2 x-3=0[/tex]
Using quadratic formula, we can solve for x.
[tex]\begin{aligned}x &=\frac{-2 \pm \sqrt{2^{2}-4 \cdot 12 \cdot(-3)}}{2 \cdot 12} \\&=\frac{-2 \pm \sqrt{4+144}}{2 \cdot 144} \\&=\frac{-2 \pm \sqrt{148}}{24} \\&=\frac{-2 \pm 2 \sqrt{37}}{24}\end{aligned}[/tex]
Taking out common term 2, we get,
[tex]\begin{array}{l}{x=\frac{-2(1 \pm \sqrt{37})}{24}} \\{x=\frac{-1 \pm \sqrt{37}}{12}}\end{array}[/tex]
Thus, the value of x is [tex]x=\frac{-1+\sqrt{37}}{12}[/tex] and [tex]x=\frac{-1-\sqrt{37}}{12}[/tex]
Segment CD has endpoints (-4, 3) and (8, -1). Find the coordinates of the point that divides the line segment directed from C to D in the ratio of 2:3.
A) (-6/5, 26/5)
B) (4/5, 7/5)
C) (1/5, 13/5)
D) (16/5, 3/5)
Answer:
B
Step-by-step explanation:
If point [tex]O(x_O,y_O)[/tex] divides the segment CD with endpoints at [tex]C(x_C,y_C)[/tex] and [tex]D(x_D,y_D)[/tex] in the ratio [tex]m:n,[/tex] then
[tex]x_O=\dfrac{nx_C+mx_D}{m+n}\\ \\y_O=\dfrac{ny_C+my_D}{m+n}[/tex]
In your case,
[tex]x_C=-4\\ \\y_C=3\\ \\x_D=8\\ \\y_D=-1\\ \\m:n=2:3,[/tex]
then
[tex]x_O=\dfrac{3\cdot (-4)+2\cdot 8}{2+3}=\dfrac{-12+16}{5}=\dfrac{4}{5}\\ \\y_O=\dfrac{3\cdot 3+2\cdot (-1)}{2+3}=\dfrac{9-2}{5}=\dfrac{7}{5}[/tex]
The sum of three consecutive integers is 42
Answer:
The integers are 13, 14, and 15.
Step-by-step explanation:
Let the smallest one be x.
Then, the other two integers are x + 1 and x + 2.
x + x + 1 + x + 2 = 42
3x + 3 = 42
3x = 39
x = 13
x + 1 = 14
x + 2 = 15
The integers are 13, 14, and 15.
4(7+v) help me please i am so confused
Answer:
28+4v
Step-by-step explanation:
multiply each term in parenthesis by 4.
multiply the numbers 4×7+4v
= the solution 28+4v
Answer:
V = -7 or 28 + 4V
Step-by-step explanation:
distribute the 4 to the 7 and V ---> 28 + 4v = 0
subtract 28 from both sides ---> 4V = -28
divide 4 by both sides --> V = -7
Please help I don’t know how to-
Answer:
y is going back by 3's x is going back one
Step-by-step explanation:
Use order of operation 3³ - (60 ÷ 10) + 8
Mr. McNeely has a wooden box in the shape of a right rectangular prism. The box measures 2
feet by 3 feet by 2.8 feet. What is the surface area of the box?
Answer:
40ft^2
Step-by-step explanation:
multiply :
2(2*3)
2(2*2.8)
2(3*2.8)
Each value in the parenthesis are the areas of 3 different sides. You then multiply by two because there is another side opposite to the side that is the same.
then add all of those up
you get 40
(8x+3)+3x what answer
Answer:
11x+3
Step-by-step explanation:
Sarah paints a straight line. The line is 13 1/2 ft long. She wants to divide the line into sections that are each 18 ft long.
How many sections will the line be divided into?
The number of sections made is [tex]\frac{3}{4}[/tex]
Solution:
Given that, Sarah paints a straight line
The line is [tex]13\frac{1}{2}[/tex] feet
She wants to divide the line into sections that are each 18 ft long
To find: Number of sections
From given,
[tex]\text{Length of line } = 13\frac{1}{2} = 13.5 \text{ feet }[/tex]
[tex]\text{Length of 1 section } = 18 \text{ feet }[/tex]
Number of sections can be found by dividing the total length of line by length of 1 section
[tex]\text{Number of sections } = \frac{\text{Total length of line}}{\text{length of 1 section}}[/tex]
Substituting the values, we get,
[tex]\text{Number of sections } = \frac{13.5}{18} = 0.75 = \frac{3}{4}[/tex]
Thus number of sections made is [tex]\frac{3}{4}[/tex]
Solve the system of linear equations by substitution 2x=12 x-5y=-29
Answer:
Step-by-step explanation:
2x = 12
x = 12/2
x = 6
And
x - 5y = -29
6 = - 5y = - 29
-5y = -29 - 6
-5y = -35
y = -35/-5
y = 7
The solution to the system of equation is (6, 7)
Given the system of equation
2x = 12 and
x - 5y = -29
From equation 1;
2x = 12
x = 6
Substitute x = 6 into equation 2:
x - 5y = -29
6 - 5y = -29
-5y = -29 - 6
-5y = -35
y = 7
Hence the solution to the system of equation is (6, 7)
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I want to do this problem in product standard form (5i-3)(2i+1)
=======================================
Work Shown:
Let x = 5i-3
That allows us to go from (5i-3)(2i+1) to x(2i+1)
Distribute the x through: x*(2i) + x*(1) = 2i*x + x = 2i(x) + 1(x)
Now we replace every x in 2i(x) + 1(x) with 5i-3, and then we distribute a second time
2i(x) + 1(x) = 2i(5i-3) + 1(5i-3)
2i(x) + 1(x) = 2i(5i)+2i(-3) + 1(5i)+1(-3)
2i(x) + 1(x) = 10i^2 - 6i + 5i - 3
2i(x) + 1(x) = 10(-1) - i - 3
2i(x) + 1(x) = -10 - i - 3
2i(x) + 1(x) = -13 - i
Therefore, (5i-3)(2i+1) = -13 - i
The result is in a+bi form where a = -13 and b = -1.
------------------
An alternative method is to use the box method. This is where you set up a grid that helps you multiply out (5i-3)(2i+1)
See the diagram below.
Each of the 4 red terms in the boxes represents the result of multiplying the outer blue and green terms. Example: 5i times 2i = 10i^2 in row1, column1.
Question 8 of 10
2 Points
Dave owns a $250,000 home, for which he has a 30-year mortgage in the
amount of $1300 a month. Once he has paid off the mortgage, how much will
he have paid in interest?
O A. $209,000
O B. $211,000
O c. $241,000
O D. $218,000
SUBMIT
Answer:D:$218,000
Step-by-step explanation:he owns 1300 monthly on the 30 year mortgage
So for a year he owes
1300*12= 15600 a year
Which will multiply by 30 years
15600*30= $468000 will be all he need to paid to cover is mortgage
To know the interest the needs to pay
Subtract the total amount from the real amount of the house
$468000-$250000= $218,000
Final answer:
Dave will have paid $218,000 in interest on his $250,000 home after making $1300 monthly payments for 30 years. The interest paid is determined by subtracting the original loan amount from the total amount paid over the mortgage term.So,option D. $218,000 is correct.
Explanation:
The question asks, once Dave has paid off his mortgage, how much will he have paid in interest for a $250,000 home with a 30-year mortgage at $1300 a month. To solve this, first, we calculate the total amount paid over the 30 years, then subtract the principal to find the interest paid.
First, multiply the monthly mortgage payment by the number of months in 30 years: $1300 × (30 × 12) = $468,000.
Next, subtract the original home value (or the principal of the loan) from the total amount paid: $468,000 - $250,000 = $218,000.
Therefore, over the course of 30 years, Dave will have paid $218,000 in interest on his mortgage.
Solve V = ℓwh for w.
w = Vℓh
Answer:
w = V/(ℓh)
Step-by-step explanation:
Divide the given equation by the coefficient of w:
V/(ℓh) = ℓwh/(ℓh)
w = V/(ℓh)
Anybody know the answer?
Answer:
C.
Step-by-step explanation:
The eqn. of a circle with centre (h,k)and radius ris given by,
Respond to the following based on your reading.
m
1. What amount of work is done when a force of 50 N is used to drag an object a distance of 20
meters across a floor?
i
2. What's the kinetic energy of an object that has a mass of 12 kilograms and moves with a velocity
of 10 m/s?
3. A skateboarder is inside
of a half-pipe, shown here.
Explain her energy
transformations as she
jumps off at point A, slides
to point B, and finally
reaches point c
G
4. If the skateboarder
continues going back and
forth on the half-pipe she'll
1) The work done is 1000 J
2) The kinetic energy is 600 J
3) There is a continuous conversion between kinetic and potential energy
Step-by-step explanation:
1)
The work done by a force when pushing/pulling an object is given by
[tex]W=Fd cos \theta[/tex]
where
F is the magnitude of the force
d is the displacement
[tex]\theta[/tex] is the angle between the direction of the force and of the displacement
In this problem, we have:
F = 50 N is the force
d = 20 m is the displacement
[tex]\theta=0[/tex], assuming the object is parallel to the displacement
Substituitng,
[tex]W=(50)(20)(cos 0)=1000 J[/tex]
2)
The kinetic energy of an object is the energy due to the motion of the object. It is given by
[tex]K=\frac{1}{2}mv^2[/tex]
where
m is the mass of the object
v is its speed
For the object in this problem,
m = 12 kg is the mass
v = 10 m/s is the speed
Substituting, we find
[tex]K=\frac{1}{2}(12)(10)^2=600 J[/tex]
3)
Here the skateboarder is moving on the half-pipe. According to the law of conservation of energy, the total mechanical energy, sum of kinetic and potential energy, is conserved:
[tex]E=KE+PE=const.[/tex]
This means that:
When the skateboarder is at the highest point of its motion, its potential energy PE is maximum, while the kinetic energy KE is zeroWhen the skateboarder is at the lowest point of its motion, its potential energy PE is zero, while the kinetic energy KE is maximumTherefore, there is a continuous conversion between potential and kinetic energy.
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Answer:
1. W = Fs
W = 50 N 20 m
W = 1,000 J
2. Ek=mv22
Ek=12kg×(10m/s2)2
Ek=12×1002
Ek=1,2002
Ek = 600 J
3. At point A, the skateboarder’s energy is all potential since she is high up (PE = mgh), and gravity has the potential to pull her down. She isn't moving, so she doesn't have velocity. Therefore, she doesn't have kinetic energy. At point B, she is moving the fastest during her ride and is as close to the ground as the ramp allows. Thus, her potential energy has been turned into kinetic energy due to her velocity and lack of height. At point C, if she comes to a stop on the other side of the half-pipe, her kinetic energy has been turned back into potential energy since she is high up again.
4. Eventually, the friction between the wheels and the ground will cause the skateboard to stop. Each time she goes back and forth, she will lose some of her initial energy from her drop-in, as long as she doesn't push off the sides at all.
Step-by-step explanation:
Penn foster :)
What is the slope of the given points (0,-1) and (-2,-4)
Answer:
y= -5/2x - -1
Step-by-step explanation:
1. Identify two points on the line
2. Select one to be (x1, y1) and the other to be (x2, y2).
3. Use the slope equation to calculate slope.
Final answer should be in the formula y=mx+b
The slope of the line passing through the points (0, -1) and (-2, -4) is calculated using the formula (Y2-Y1)/(X2-X1) and results in a slope of 1.5.
Explanation:To find the slope of the line passing through two points, you can use the slope formula:
m = (Y2-Y1)/(X2-X1)
Applying this formula to the given points (0, -1) and (-2, -4):
Calculate the difference in the y-coordinates (rise): -4 - (-1) = -4 + 1 = -3.
Calculate the difference in the x-coordinates (run): -2 - 0 = -2.
Divide the rise by the run to get the slope: -3 / -2 = 1.5.
Thus, the slope of the line passing through the points (0, -1) and (-2, -4) is 1.5.
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There are 30 major league baseball teams and 32 national football league teams. The expanded roster for major league baseball teams is 40 players and it is 53 for national football league teams. How many more players are in the national football league than in major league badeball?
To find out how many more players are in the NFL than in the MLB, calculate the total number of players in each league and then subtract. This results in 496 more players in the NFL.
Explanation:To determine how many more players are in the National Football League (NFL) than in Major League Baseball (MLB), you need to apply basic multiplication and subtraction.
Calculate the total number of players in MLB: The expanded roster for each MLB team is 40 players. There are 30 MLB teams. So, multiply 40 by 30 to get 1200 players.Calculate the total number of players in NFL: The expanded roster for each NFL team is 53 players. There are 32 NFL teams, so multiply 53 by 32 to get 1696 players.Find the difference: Subtract the total number of MLB players from the total number of NFL players to find the difference. So, 1696 - 1200 = 496 players.Therefore, there are 496 more players in the NFL than in the MLB.
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There are 496 more players in the National Football League than in Major League Baseball.
To find out how many more players are in the National Football League (NFL) compared to Major League Baseball (MLB), we will first calculate the total number of players in each league.
Step 1: Calculate the total number of players in each league
NFL:
Number of teams: 32Players per team: 53Total players in NFL:MLB:
Number of teams: 30Players per team: 40Total players in MLB:Step 2: Calculate the difference in total players
To find out how many more players are in the NFL than in the MLB, we subtract the total number of MLB players from the total number of NFL players:Conclusion
Thus, there are 496 more players in the National Football League than in Major League Baseball.
What is the solution
3x-2y=14
5x+y=32
Answer:
solution is (6,2)
Step-by-step explanation:
3x - 2y = 14
5x + y = 32....multiply by 2
------------
3x - 2y = 14
10x + 2y = 64 (result of multiplying by 2)
------------add
13x = 78
x 78/13
x = 6
5x + y = 32
5(6) + y = 32
30 + y = 32
y = 32 - 30
y = 2
How do I solve
2(x+y)^2+(x+y)-6 ????
Answer:
2x2+4xy+2y+x+y−6
Step-by-step explanation:
Hope this helps!
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Complete the equation of the line through (3, -1) and (4, 7)
Answer:
y = 8x -25
Step-by-step explanation:
The two-point form of the equation of a line can be used.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
y = (7-(-1))/(4-3)(x -3) +(-1)
y = 8(x -3) -1
y = 8x -25 . . . . slope-intercept form of the equation
_____
We don't know what you're starting with, so we don't know how to "complete the equation." Perhaps the above equation is sufficient for the task.
The ratio of the angle measures in a triangle is 4:5:9. What is the measure of each angle
Answer:
40, 50, and 90
Step-by-step explanation:
You know that there are 180 degrees in a triangle, so you'd use the ratio to find each angle by setting up your equation like this: 4x+5x+9x=180
Then, simplify the equation and solve for x:
18x=180x=10Then, plug 10 into each x value to find each angle measure:
4(10)=40, 5(10)=50, 9(10)=90
Final answer:
The measures of the angles in a triangle with a ratio of 4:5:9 are 40 degrees, 50 degrees, and 90 degrees respectively, calculated by dividing 180 degrees by the sum of the ratios and then multiplying by each individual ratio.
Explanation:
The question is asking us to find the measure of each angle in a triangle when the ratio of the angle measures is given as 4:5:9. To solve this, we will use the fact that the sum of the angles in any triangle is 180 degrees.
First, let's add the ratios together (4+5+9=18) to find the total number of parts that divide the 180 degrees. Now, divide the total degrees (180) by the number of parts (18) to find the measure of one part, which is 10 degrees. Then, multiply the value of one part by the number of parts for each ratio: 4 parts, 5 parts, and 9 parts.
The measure of the first angle (4 parts) is 4 x 10 = 40 degrees, the second angle (5 parts) is 5 x 10 = 50 degrees, and the third angle (9 parts) is 9 x 10 = 90 degrees. Hence, the measures of the angles in the triangle are 40 degrees, 50 degrees, and 90 degrees respectively.
While in Brazil, Jacob exchanged some
American dollars for Brazilian currency,
Brazilian real. He was given 45 Brazilian
real for $55. What was the approximate
exchange rate for Brazilian real per
dollar?
Answer:
1:1.22 Look at explanation and picture.
Step-by-step explanation:
If Jacob was given 45 Brazilian currency items for $55 you would need to divide 55 by 45 to see how much American dollars it would take to recieve one Brazilian currency.
For one Brazilian currency you need about (fig A) american currency for 1 brazilian currency.
The exchange rate for Brazilian real per American dollar for Jacob's transaction is approximately 0.8182 real per dollar, calculated by dividing the total amount of reals received by the dollars exchanged.
Explanation:To calculate the exchange rate of Brazilian real per American dollar for Jacob's currency exchange, we divide the amount of Brazilian real he received by the amount of American dollars he exchanged. Jacob received 45 Brazilian real for $55 US dollars. The calculation to find the exchange rate is as follows:
Determine the total amount of Brazilian real received: 45 real.Determine the total amount of American dollars exchanged: $55.Divide the amount in real by the amount in dollars to find the exchange rate: 45 real / $55 = 0.8182.The exchange rate is approximately 0.8182 Brazilian real per American dollar.It is important to compare this rate with the market rates mentioned, such as 35 cents/real or the government-set rate of 30 cents/real. It can be observed that Jacob's exchange rate is different from these rates, which illustrates how actual exchange rates may vary due to different factors such as service charges or varying rates across different currency exchange venues.
A survey asked 40 students If they play an instrument and if they are in band.
1.25 students play an instrument.
2. 20 students are in band.
3. 20 students are not in band.
Which table shows these data correctly entered in a two-way frequency table?
Answer:
The correct answer is,
The two-way frequency table is given as:
Band Not in Band Total
Play instrument 20 5 25
Do not play instrument 0 15 15
Total 20 20 40
Step-by-step explanation:
Given that;
We are given a survey of 40 students regarding whether they play an instrument or not.
We are given an information as:
1. 25 students play an instrument.
2. 20 students are in band.
3. 20 students are not in band
Hence, the table can be formed as:
Band Not in Band Total
Play instrument 20 5 25
Do not play instrument 0 15 15
Total 20 20 40
Since, those who don't play any instruments can't even play band hence the value of that in table is 0.
Thus, Option C is correct.
Lines b and c are parallel. Horizontal and parallel lines b and c are cut by transversal a. Where line b intersects line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 1, 2, (18 x + 4) degrees, (7 x + 1) degrees. Where line c intersects line a, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 5, 6, 8, 7. What is the measure of Angle2? mAngle2 = 31° mAngle2 = 50° mAngle2 = 120° mAngle2 = 130°
Answer:
mAngle2 = 50°
Step-by-step explanation:
A relative schematic has been attached bellow describing the problem.
In this case, we will be working with Supplementary angles. The latter denote angles which when summed together equal to 180°.
From the schematic we can identify the following Supplementary pairs as:
∠1 and ∠2
∠2 and ∠(18x+4)
∠(18x+4) and ∠(7x+1)
∠(7x+1) and ∠1
So lets start by finding the value of [tex]x[/tex] as follow. Since we know the supplementary pairs we have that
[tex](18x+4)+(7x+1)=180\\18x+7x+4+1=180\\25x+5=180\\25x=180-5\\25x=175\\x=\frac{175}{25} \\x=7[/tex]
Now we similarly know that ∠2 and ∠(18x+4) are supplementary. So lets replace the value of [tex]x[/tex] in ∠[tex]18x+4[/tex], we have
[tex]18(x=7)+4=126+4=130[/tex]
So finally we have
[tex]<2 + 130=180\\<2=180-130\\<2=50[/tex]
Thus we can say that ∠2 = 50° (which matches the second options from the available ones).
Answer:
50
Step-by-step explanation:
8W - 7w + 9 - 2 combining like terms
Answer:
The answer is 1w+7
Step-by-step explanation:
you first combine 8w and -7w to get 1w then you combine 9 and -2 to get 7
Bartering was an early way that people _____.
1.exchanged currency in the form of paper or metal
2.exchanged a good or service directly for a good or service
3.talked to each other
4.shared financial information over long distances
Answer:
#2
Step-by-step explanation:
N/A
Bartering was an early way that people exchanged a good or service directly for a good or service. (option 2)
Bartering, the act of exchanging goods or services directly for other goods or services, was an early way that people engaged in trade and commerce.
Before the advent of standardized currency in the form of paper or metal, societies relied on bartering as a means of acquiring what they needed.
In a barter system, individuals would negotiate the exchange of items they possessed, often based on their mutual needs and values.
Hence the correct option is (2).
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Use the grouping method to factor this polynomial completely 3x^3+12x^2+2x+8
Answer:
(x+4)(3x^2 + 2)
Step-by-step explanation:
3x^3+12x^2+2x+8
3x^2(x + 4) + 2(x + 4)
(x+4)(3x^2 + 2)
The total number of burgers sold from a restaurant from Monday to Sunday can be modeled by the function f(d)=200d3+542d2+179d+1605and the number of visitors to the restaurant from Monday to Sunday can be modeled by g(d)=100d+321, where d is the number of days since Monday. What is the average number of burgers per person?
Answer:
[tex]2d^2-d+5[/tex]
Step-by-step explanation:
The total number of burgers sold from a restaurant from Monday to Sunday:
[tex]f(d)=200d^3+542d^2+179d+1605[/tex]
The number of visitors to the restaurant from Monday to Sunday:
[tex]g(d)=100d+321[/tex]
To find the average number of burgers per person, just divide [tex]f(d)[/tex] by [tex]g(d).[/tex]
First, multiply [tex]g(d)[/tex] by [tex]2d^2[/tex] and subtract the result from [tex]f(d)[/tex]:
[tex]200d^3+542d^2+179d+1605-2d^2(100d+321)\\ \\=200d^3+542d^2+179d+1605-200d^3-642d^2\\ \\=-100d^2+179d+1605[/tex]
Then, multiply [tex]g(d)[/tex] by [tex]-d[/tex] and subtract the result from [tex]-100d^2+179d+1605[/tex]:
[tex]-100d^2+179d+1605-(-d)(100d+321)\\ \\=-100d^2+179d+1605+100d^2+321d\\ \\=500d+1605[/tex]
Now, multiply [tex]g(d)[/tex] by [tex]5[/tex] and subtract the result from [tex]500d+1605[/tex]:
[tex]500d+1605-5(100d+321)\\ \\=500d+1605-500d-1605\\ \\=0[/tex]
Hence,
[tex]f(d)=g(d)(2d^2-d+5)[/tex]
and the function
[tex]b(d)=2d^2-d+5[/tex]
represents the average number of burgers per person.
16+13p-9p write an equivalent expression by combining like terms
Solve log x=5 will mark brainliest
Answer:
100000
Explanation:
We have the natural base of the log; 10.
Now, since we are solving for the value that is being "logged"
we can say 10 to the power of 5 equals.... what?
10^5 is 100000, x 100000.
Hope this helps!
How many x-intercept does the graph of y=2^2+5x+9
Answer:
there is only one x-intercept. The x-intercept is 2.6.
Step-by-step explanation: